The world number two fought back from a set down twice, forcing the Brit in to a deciding set.
Read how all the action unfolded below:
8.09amGood morning. The second of the men's semi-finals is due to get underway in the next half hour, and it should be a cracking match between the second and third seeds.
8.11amMurray and Federer have played each other 19 times, with Murray having won 10 times. However, he's never beaten his Swiss opponent in a Grand Slam.
8.13amThe Scot has had a fairly straight-forward route to the last four, and is the only player in the men's draw not to have dropped a set to reach this stage.
8.15amFederer made it to the quarters without trouble, but was taken to five sets against Jo-Wilfried Tsonga just two days ago, spending over three and a half hours on court.
8.17amMurray spoke to Eurosport ahead of his match. When asked about the advantages of an easier route to the semis, he said: "You haven't used up too much energy, mentally pretty fresh because I haven't been under too much pressure in any matches. I'll need to make sure I'm really focused in the next match because obviously it will be tougher."
8.18amIn preparation for this match, the Scot has practiced on the Hisense Arena and the Rod Laver Arena at night. This will be his first night match during the tournament, while all of Federer's have been during the evening session.
8.22amThe second seed believes that he knows Murray's game well. After his last match, he said: "I know what to expect; whereas it would be different if I hadn't played him. Because he has changed his game around a bit, he's playing more offensive. I'm looking forward to it."
8.26amIf Murray makes the final, he will be playing to become the first man to win his second Grand Slam at the tournament immediately after the Slam where he won his first.
8.31amFederer has won 17 Grand Slam titles in his career, including four times at the Australian Open. However, only two of those 17 have come in the last three years.
8.34amFour-time Australian Open champion Andre Agassi will be presenting the winner of Sunday's final with the trophy. He's predicting a win for Murray today.
8.35amThe players have just walked out in to the Rod Laver Arena. There a big cheers for both players, but it was a little louder for Federer, and there are a good number of Swiss flags in the crowd.
8.39amThere are lots of Scottish fans there too. Earlier today, Judy Murray, Andy's mother and Britain's Fed Cup captain, tweeted: "Gotta love the Scottish support at Melbourne Park.......x". The message was accompanied by a picture of five fans, each wearing a t-shirt with a different letter, spelling "Muzza".
8.40amMurray won the toss and chose his end rather than whether he wanted to serve first or second. The players with now have a couple of minutes to warm up before the match gets underway.
8.43amThere's a bit of confusion over Murray's decision to chose his end. His brother Jamie, working as a TV pundit for this match, is baffled by the move, saying he's never known a singles player to chose an end over serve. However, the weather forecast shows that there are winds of 35kph around the stadium, maybe that's a factor for the Brit.
8.44amPlay is just about to get underway, with Federer serving first.
Murray *0-1 FedererNot a bad start for Murray. He beats Federer with an aggressive forehand shot, before an unlucky bounce off the net chord takes Federer's backhand wide. A long shot at the end of a 28-stroke rally gave the Scot a break point, but it was easily saved by the second seed with a volley in to the open court. A long forehand from Murray and a fantastic forehand winner from Federer allow him to hold the opening game, but it looks like Murray is keen to get a break early in this first set.
Murray 1-1* FedererAn easy start on serve for Murray sees him comfortably take the game. A correction from the umpire in the Scot's favour is met with irritation from Federer, but he lets the call stands and doesn't challenge, giving Murray a 40-15 lead, before missing the return against a big serve to give Murray the game.
Murray *2-1 FedererBREAK! Already, we're seeing some lengthy rallies against the Federer serve. After a long quarter-final, the 31-year-old won't be enjoying them. A 22-shot rally ends with the Swiss putting the ball in to the net, giving Murray two break points. He wastes the first with a wild forehand which flies well long of the baseline, and gets the second caught of the net to take the game to deuce. Murray continues to get the better of Federer in rallies, giving himself another break point, which he takes when the second seed unleashes a low backhand, which fails to clear the net.
9.01amMurray needed four break points in that game before he managed to get the better of Federer. He's certainly playing the better tennis at the moment, but he needs to make sure he makes the most of his chances while he has them.
Murray 3-1* FedererMurray races to a 40-0 lead, finding a 212kph ace along the way, but a long forehand and a low backhand allow Federer back in to the game. Murray then misses a volley, dragging it wide, to give Federer deuce. The Scot fails to clear the net again to give the Swiss a chance to break back straight away, but he finds another ace. Federer is unable to return another big serve from the world number three, sending it long to give Murray the game.
Murray *3-2 FedererFederer looks comfortable on serve for the first time in the match, quickly finding 40-0 before Murray mis-reads his serve and is unable to get the return in to allow Federer to hold. For the last two games, Federer has been at the end that Murray chose to start the match at, so it looks like the Brit was right that there is an advantage to playing that side of the court.
Murray 4-2* FedererFederer takes a lead in the game when Murray sends his forehand long. Some strong serves quickly turn it around for the Scot, and he takes the game.
Murray *4-3 FedererMurray uses his full range of shots to bring up two break points. Federer smashes the ball in to the open court, Murray gets to it but his return finds the net. The second seed sends the Scot out wide, but Murray recovers well to make the return, but it's a fraction wide, taking the game to deuce. The Swiss finds a couple of well-placed serves to take the hold. Murray's let him off the hook there, he would have been serving for the set next if he'd managed to get the break.
Murray 5-3* FedererIt's an easy game for Murray. Federer is caught out by the net to give Murray the game, but it's been the number of winners from the Scot that have put him in charge in this first set. Murray has 13 to Federer's five.
Murray *5-4 FedererFederer holds his service game fairly comfortably, forcing Murray to try to serve the set out in the next game. The world number two has only threatened the Brit's serve once so far in this match.
9.30amSET! Murray 6-4 Federer
9.31amMurray starts well, firing an ace past his opponent. Federer uses his full range of weapons to fight back, taking a point from an 18-stroke rally. However, Murray ups the power on his serve, and there's little the Swiss player can do on the return. Murray takes the game and the first set.
9.33amThere had been some concern that Murray's easy passage to the last four would hinder him when he came up against a strong opponent, but that doesn't seem to be the case so far in this match. There have been plenty of lengthy rallies early on, and it's definitely played into the Scot's hands.
Murray 6-4 *0-1 FedererFederer looks to have started well, finding himself up 40-15, but another good rally from Murray and the first double fault of the match brings up deuce. Federer responds with his first ace of the match, but fires his forehand wide on the next point, but he finds a couple of good shots to take the game.
Murray 6-4 1-1* FedererFederer is starting to look a little sharper during rallies, duping his opponent with a cross court backhand. Murray's serve it too good though, he finds two aces to add to a long shot from Federer to take the game.
Murray 6-4 *1-2 FedererFederer serves up his second double fault, but finds his form towards the end of the game, finishing with an ace. The second seed is starting to find his way in to this match.
Murray 6-4 2-2* FedererMurray takes a 30-0 lead, before making Federer work hard behind the baseline in a 16-shot rally, but it's the world number two who takes the point in the end, just finding the sideline with a brilliant forehand. Federer looks to recreate the shot on the next point but it goes wide, and a big serve from Murray sees the Swiss put the ball in the net to give the Scot another hold of serve.
Murray 6-4 *2-3 FedererMurray shows off his pace, traveling the width of the court to make a stunning return for a 30-0 lead. A couple of mistakes from the British number one let Federer back in to the game. At deuce, Murray sends his forehand return long allowing the second seed to secure the hold with an ace on the next point.
Murray 6-4 3-3* FedererMurray open with a sensational volley, but a couple of errors keep Federer in the game at 30-30. The third seed slices his backhand low, but Federer's return is too low, getting stuck on the net. The Scot ends with an ace to keep the set level.
Murray 6-4 *3-4 FedererA brilliant rally opens the game. It's Murray that gets the point, finishing with a superb cross-court backhand. A couple of mistakes see Murray have one of his trademark arguments with himself. Another couple of missed returns give Federer the game. The Brit was definitely looking to attack, but tried to use too much power.
Murray 6-4 4-4* FedererMurray channels his disappointment from the last game to find a series of big, non-returnable serve, giving Murray a 40-0 lead. Federer gets the ball back in play, engaging the Brit in another lengthy rally, but it's the third seed who comes out on top this time to take the game.
Murray 6-4 *4-5 FedererFederer has been so much stronger on serve in this set than in the third. Murray returns well, but the Swiss is always in control of the game, dictating the pace of the rallies for an easy hold. Murray needs to take the next game to stay in the set.
10.08amMurray is yet to face a tiebreak during this tournament. Federer has been involved in four on his route to the semis, winning them all.
Murray 6-4 5-5* FedererAn ace gets the game underway for Murray. Both players find a series of sublime shots in a lengthy rally, but Murray edges the ball wide, attempting a tricky backhand. He challenges, but hawkeye shows that the ball was milimetres out. Murray misses his first serve, but Federer's return on the second serve is long, resulting in some slightly colourful language from the second seed, and Murray takes another game.
Murray 6-4 *5-6 FedererFederer's frustrations are channeled well to give him an easy hold. At the very least he'll get a tiebreak from the second set, after looking off the pace in the opening set.
Murray 6-4 6-6 FedererMuuray's serve has been almost untouchable throughout this match so far. He finishes the game with two aces. After 12 games, there's nothing between the two players, so they head to a tiebreak.
TIEBREAKMurray *1-0 Federer
TIEBREAKMurray *1-1 Federer
TIEBREAKMurray 1-2* Federer - all points against serve so far!
TIEBREAKMurray 1-3* Federer
TIEBREAKMurray *1-4 Federer
TIEBREAKMurray *2-4 Federer
TIEBREAKMurray 3-4* Federer
TIEBREAKMurray 4-4* Federer
TIEBREAKMurray *4-5 Federer
TIEBREAKMurray *5-5 Federer
TIEBREAKMurray 5-6* Federer - set point for Federer on his own serve.
10.28amSET! Murray 6-4 6-7 Federer
10.29amAfter a strong start to the tiebreak by Federer, Murray fought back hard to get it back on serve, but a badly-times jump meant he was off balance for a smash past his Swiss opponent at 5-5, allowing Federer to bring up set point on his own serve.
10.31amMurray was by the stronger of the two players in the first set, but Federer has found his way in to this match, and will have all the momentum heading in to the third set. However, Federer's extra time on court in the last round could come in to play, with this match rapidly approaching the two hour mark, with at least another two sets to play.
Murray 6-4 6-7 1-0* FedererMurray starts the third set with a reasonable service game. Federer gets a couple of points on the board, but the Scot never looked in any danger of being broken. He'll be keen for an early break against the Swiss serve though to get control of the match back.
Murray 6-4 6-7 *1-1 FedererA brilliant opening rally from Murray catches Federer out, before the second seed misses a backhand from the baseline. Federer gets back in to the game with one of his fastest serves of the match, followed by a brilliant volley. Another lengthy rally ends when Federer fires his forehand wide, giving Murray break point, but a shot from the Brit goes well wide to bring up deuce. Federer ups the power on his serve to force his way to a hold.
Murray 6-4 6-7 2-1* FedererFederer struggles with his returns, firing Murray's first three serves straight in to the net. He gets the ball back in play at 40-0 but misses a backhand, rounding off an easy hold for Murray.
Murray 6-4 6-7 *2-2 FedererAs the game goes in to its third hour, Murray encounters the same problem as Federer, he can't get Federer's serve back in play. There's a bit a sense that both player might have eased off a little in the last couple of games as they realise they may be on court for quite some time yet.
Murray 6-4 6-7 3-2* FedererFederer throws in a drop shot, which catches the Scot out. Murray looks to take a 40-15 lead, but puts too much behind his backhand and the ball goes wide. A long shot from Federer puts Murray back ahead, before the third seed smashes a volley beyond the Swiss, keeping the third set with serve.
10.52amDuring that game, there were a couple of shots of Andy Murray's coach Ivan Lendl, one after Murray lost a shot, and one when he went 4-30 up. Unsurprisingly, his expression was unchanged for both.
Murray 6-4 6-7 *4-2 FedererBREAK! A messy start to the game from Federer gives Murray a 30-0 lead. The second seed sends his forehand long to give Murray three break points, and takes his frustrations out on the umpire. A long shot from the Scot saves the first break point for Federer, but then a lazy forehand drifts wide, putting Murray a break up in the third set.
Murray 6-4 6-7 5-2* FedererMurray has rediscovered the brilliance that he showed in the first set of this match, racing to a 5-2 lead with an easy hold which included two aces from the British number one. Federer is not looking happy with himself at the moment.
Murray 6-4 6-7 *5-3 FedererMurray makes Federer work to hold the game, but hold he does. Murray will now serve for a two sets to one lead, having faced, and saved, just the one break point so far.
11.04amSET! Murray 6-4 6-7 6-3 Federer
11.05amFederer's returns were better during the last game, but that merely allowed Murray to show his dominance in the rallies, before clipping the centre line on his serve to take the third set with an ace. Murray nips off court after securing the 2-1 lead for a quick break.
11.07amMurray is back on court, but now Federer's gone for a break too. Apparently there is only one rest room for the players on court.
11.08amBoth players are back, are the fourth set is about to get underway, Federer serving first.
Murray 6-4 6-7 6-3 *0-1 FedererFederer's serve is no match for Murray's ability to return, and the Swiss player faces a break in the first game of the match. While trying to change direction behind the baseline, Murray loses hit footing. It doesn't look like he's hurt, but he has a good curse at his footwear anyway. The missed break allows Federer to dig deep and serve out the game.
Murray 6-4 6-7 6-3 1-1* FedererA great return from Federer allows him to dictate the rally, sending Murray all around the court before taking the point. At 30-30, the Brit plays a risky forehand, but it clips the sideline, allowing him to take the game on the next point. It was one of the third seed's weaker service games during this match, but he got the job done.
Murray 6-4 6-7 6-3 *1-2 FedererIt's a much better service game from Federer this time around. The world number two hits some fantastic shots to force errors from his opponent, and also finds a brilliant overhead forehead winner to keep the fourth set with serve.
Murray 6-4 6-7 6-3 1-3* FedererBREAK! Murray is furious with himself after a couple of unforced errors allow Federer to take a 30-0 lead. Despite giving himself a talking to, the Scot sends his forehand long, giving Federer three break points. A big serve saves the first, followed by an ace to take the game to 40-30. On the third break point, Murray runs his forehand wide, and Federer breaks for the first time during this match.
Murray 6-4 6-7 6-3 *1-4 FedererThe break has given Federer a boost, while Murray has gone off the boil a little. The Swiss plays some sensational tennis to race to a 40-0 lead, and takes the game with some stunning play from the baseline.
Murray 6-4 6-7 6-3 2-4* FedererMurray comfortably holds serve. His serve doesn't look the weapon it was in the first three sets at the moment, but it's still strong enough that Federer has to work hard to make a return, with the Swiss claiming just one point off the game.
Murray 6-4 6-7 6-3 *3-4 FedererBREAK! In contrast to Murray's dip during service games, Federer is serving better now than at any point during the previous three sets. However, a poor drop shot from the second seed, followed by a stunning backhand from the Scot brings up break point. He dictates the rally, sending Federer the full width of the baseline, and it's too much for the Swiss. Murray is right back in this set.
Murray 6-4 6-7 6-3 4-4* FedererA closely-fought game sees Federer bring up break point with a superb curling forehand, which just clips the sideline. However, the game heads to deuce when a quick return from Murray catches his opponent out, resulting in a wide shot. The Brit takes advantage, landing his forehand just on the line at the end of a 17-shot rally. Murray loses his cool when a late call from line judge results in some confusion, with the points eventually being awarded to Federer to take the game back to deuce. The fired-up Brit channels his anger well, forcing errors from his opponent to take the game.
Murray 6-4 6-7 6-3 *4-5 FedererMurray starts the game well, hitting a pair of superb forehands to take a 30-0 lead. Federer fights back before the game heads to deuce. The Swiss takes advantage with a cross-court shot clipping the sideline, then Murray putting the ball in the net on the next point.
11.56amBoth players have let their emotions show at times during this match. If you want to see some more angst from this year's Australian Open, check out this video of the best racquet smashes from the 2013 event.
Murray 6-4 6-7 6-3 5-5* FedererMurray will be relieved to take an easy hold after his last service game. Despite a slow second serve from Murray, a backhand from the Brit gets the better of Federer, who doesn't pick up a single point in the game.
Murray 6-4 6-7 6-3 *6-5 FedererBREAK! Murray is on the attack early, keen to avoid another tiebreak against the second seed. A long forehand from Federer brings up three break points for the Brit, who has been moving around the court superbly during the last couple of games. A sliced forehand from Federer goes wide, and Murray will serve for the match.
12.07pmA perfectly timed backhand gives Federer break point at 40-30.
Murray 6-4 6-7 6-3 6-6 FedererBREAK! Murray takes the first point with a brilliant forehand to finish another lengthy rally between this pair. Another exchange between the two ends when the Scot puts the ball long, but he follows it up with a big serve, that Federer puts in the net. The world number two fights back, bringing up a break with a backhand before Murray puts the ball long. And it's another tiebreak.
TIEBREAKMurray *0-1 Federer
TIEBREAKMurray *0-2 Federer
TIEBREAKMurray 1-2* Federer
TIEBREAKMurray 2-2* Federer
TIEBREAKMurray *2-3 Federer
TIEBREAKMurray *2-4 Federer
TIEBREAKMurray 2-5* Federer
TIEBREAKMurray 2-6* Federer - four set points for the world number two!
12.15pmSET! Murray 6-4 6-7 6-3 6-7 Federer
12.16pmOnce again, Federer is commanding in the tiebreak, leveling the match at two sets each. The crowd have been supporting whichever player has been behind all match, they wanted a fifth set from the start and they've got their wish.
12.18pmMurray's serve was not as potent in the fourth set as it hand been earlier in the match. The Brit got just 53% of his serves in, winning only 58% of his points on his first serve. At least he knows he won't be facing another tiebreak.
Murray 6-4 6-7 6-3 6-7 1-0* FedererMurray misses another couple of first serves, but when he does get it in, Federer struggles on the return, and it's a fairly comfortable hold for Murray.
Murray 6-4 6-7 6-3 6-7 *2-0 FedererBREAK! Federer is also having problems getting his first serve in, and Murray takes full advantage, bringing up a break point. A couple of great returns from the Scot result in Federer forcing the ball long, giving the third seed the early advantage in this final set.
Murray 6-4 6-7 6-3 6-7 3-0* FedererFederer is starting to look a little weary as Murray sends him running from one end of the baseline to the other, reaching the ball late a couple of times. At 40-0 down, Federer attempts a drop shot, but it doesn't come off. The British number one is flying at the minute.
Murray 6-4 6-7 6-3 6-7 *3-1 FedererAt 30-30, Federer comes in to the net. Murray tries to slice his backhand past him, but it hits the net, denying the Brit a break point. Murray fights back to deuce, but two big serves from the Swiss get him on the board in the fifth set.
Murray 6-4 6-7 6-3 6-7 4-1* FedererAnother clinical display from Murray on serve, he seems to have rediscovered his rhythm. Federer makes some good returns, but struggles to get on the attack.
Murray 6-4 6-7 6-3 6-7 *4-2 FedererFederer is not done yet. He races through his service game with some brilliant ground strokes, clearly keen to get another shot at the Murray serve.
Murray 6-4 6-7 6-3 6-7 5-2* FedererMurray finds another two aces, taking his total for the match to 21. Federer is clearly on the attack, but there's little he can do when Murray serves this well. The Scot is just one game away from the final.
12.43pmTwo match points for Murray!
12.45pmGAME, SET AND MATCH! Murray 6-4 6-7 6-3 6-7 6-2 Federer
12.45pmHe's done it. Andy Murray will play Novak Djokovic in the final of the Australian Open after beating Roger Federer in five sets, taking four hours to do so.
12.46pmMurray made a bright start in the final game, catching Federer out with a brilliant return, before the clearly fatigued Swiss player fired the ball long. Another mistake allowed Murray to bring up match points, converting the second when Federer sent the ball long.
12.48pmAskes on-court after the match if his success from last year helped in this match, Murray said: "I think that that all helps, I've been known for losing tough matches, I'd never beaten Roger in a big match until the Olympics."
12.50pmWhen asked about Djokovic, he added: "This has been the court he's played his best tennis on, he's got three Australian Opens, this is his third final in a row. Every time we play each other it's normally a very physical match. I hope it's a painful match, that means it will be a good one."
12.52pmMurray will need a good recovery routine to be fresh for Sunday, but his final opponent has proved that you can play well following a marathon match. If the US Open final is anything to go by, it should be another thriller on Sunday.
12.53pmThat's all from the Australian Open today. We'll have plenty of reaction to today's play. Join us again tomorrow for the women's singles final between defending champion Victoria Azarenka and Li Na. Until then, thanks for joining us, good bye.