The 17-time Grand Slam champion breezed through the opening two sets with some dominant, attacking tennis, before Murray fought back from two match points down to edge a tie-break in the third set.
Murray survived six break points in an exhausting 20-minute game at the start of the fourth, but Federer eventually regained control to record a 6-3 6-4 6-7 6-3 win to move through to a last-four encounter with Rafael Nadal.
Read below to see how the action unfolded on the Rod Laver Arena.
8.34amWell folks, it doesn't get much better than this for a Wednesday morning. We've got Murray, the reigning Wimbledon champion who has eased himself back from back surgery, against the 17-time Grand Slam champion who rolled back the years to defeat Jo-Wilfried Tsonga a couple of days ago. It should be a cracker!
8.36amI think that the players have caught everyone by surprise. It was scheduled to start shortly after 8.30am GMT, but the Rod Laver Arena is only half-full after the conclusion of the Rafael Nadal and Grigor Dimitrov match. Nevertheless, the warm-up has been completed and we are ready to go!
Murray *0-1 FedererMurray starts with a backhand winner, but Federer forces him into a couple of errors at the back of the court. It's been an aggressive start from Murray, but he just misses with a cross-court backhand. Federer completes the game with an ace. Intriguing start.
Murray 1-1* FedererIt's a shocking start from Murray on serve, who hooks a backhand wide after tamely finding the net with the same shot. However, the Scot finds a first serve to halve the deficit, before Federer dumps a shot into the net. The Swiss then proceeds to marginally miss the right-hand corner by inches with two shots from the baseline, and Murray comes through with the hold. He hasn't quite settled just yet though.
Murray *1-2 FedererFederer sends down two aces on the way to reaching 40-0, but Murray fires back with a backhand volley at the net. It doesn't halt the Federer momentum, however, and the 17-time Grand Slam winner flicks a forehand behind the Scot to take the game.
Murray 1-3* FedererBREAK! The Wimbledon champion starts the game with an ace, but here comes Fed, who smashes his way to 15-30 before advancing into court to put away a volley. The Swiss has two break points, and he secures the early advantage with ease after Murray sends a forehand long.
Murray *1-4 FedererA miscued forehand gives Murray a chance at 30-15, but that is quickly taken away by a big first serve and an ace. Federer is on top on the Rod Laver Arena.
Murray 2-4* FedererMurray starts passively, but a forehand winner and an ace help the Scot to 30-15. Federer takes the next point, and forces the issue at 30-30, but Murray passes him with an excellent forehand down the line. The Swiss then loops a backhand long of the baseline, and Murray remains in the set.
Murray *2-5 FedererFederer crunches a backhand down the line for 15-0, but proceeds to net to give Murray a sniff at 15-15. The Scot misses with a cross-court backhand, but he succeeds on the next for 30-30. This is better! But that's even better from Federer, who plays the most immaculate of drop shots that has Murray scampering towards the net. A forehand deep into the court then has Murray on the defensive, and the former world number one is closing in on this first set.
Murray 3-5* FedererMurray attempts to take the initiative from the back of the court but only succeeds in netting, but a big first serve get him back on level terms. A couple of easy points for the Scot earn him two game points, which is taken on the first when Federer nets.
Murray *3-6 FedererSET! Wow! Federer plays a sensational drop-shot to repel Murray's excellent defensive work, before the Swiss moves the Scot around the court to force a mistake on the lob. The Swiss then thunders a huge forehand winner into the corner for three set points. That brought a roar from Federer. The set is sealed when Murray misses with a return. This is going to be tough for the Wimbledon champion. Federer is relentless.
Murray 3-6 1-0* FedererMurray screams "come on!" after taking the first point, and it gets him on the way to 30-15. Federer makes it 30-30, but what a point on the next! A 23-shot rally sees Murray fail to convert a comfortable volley, but he recovers to force Federer to net. That was a massive point! An ace out wide seals the game.
Murray *3-6 1-1 FedererHow's your luck? A point-winning shot from Murray from the baseline is called out, but he correctly challenges. However, the re-played point sees Federer hit an ace. Ouch. The pair share unforced errors to allow Federer to move to 30-15, before a fourth ace from the Swiss brings up two game points. A fine one-two takes the game, and you get the feeling that Murray is going to do well to break serve in this match.
Murray 3-6 2-1* FedererThat's delightful from Murray, who produces the perfect lob over Federer, but the Swiss replies with an outrageous forehand up the line. This is warming up now. Murray has two game points, but a shocking forehand finds the bottom of the net. However, a big serve from Murray finds its target, and we remain on the serve at the start of the second.
Murray *3-6 2-2 FedererI get the impression that Murray knows what he needs to do off the Federer serve, but he isn't executing the plan at the moment. However, he is helped out by a couple of mistakes by his opponent, and the Scot has 15-30. Federer eases to 30-30, but Murray misses a huge opportunity for a break point when missing with a cross-court forehand return. That's the chance come and gone.
Murray 3-6 2-3* FedererBREAK! Federer comes out firing at the start of the game, but a Murray ace down the middle gives him a 30-15 advantage. However, the Scot succumbs on the next two points, dumping a forehand into the net to hand a break opportunity to Federer. This is big. Murray finds the first serve, but he goes for too much on the forehand and it's wide! Federer breaks.
Murray *3-6 2-4 FedererFederer begins the game with an ace, but a wayward forehand levels it up. The Swiss clips the line with a forehand winner, before Murray floats a return long. However, a magical lob is appreciated by Federer, who then slices a backhand wide. We have deuce! The pair trade points for a second deuce, but two huge serves from the Swiss help him regain his stranglehold on this match.
Murray 3-6 3-4* FedererMurray powers down an ace for 15-15, but the crowd are on their feet for a simply ridiculous backhand half-volley from Federer. It was sublime. However, the Scot secures a huge hold of serve, recording three successive points with an ace taking him back to within one of the Swiss.
Murray *3-6 3-5 FedererMurray takes the first point after some fine coverage at the net, and the Scot has 15-30 after the Swiss frames a forehand from the baseline. But that's poor from Murray, who floats a second-serve return over the line. He shouts "stupid!" at himself. He was right, too. Two more mistakes from Murray gift the game to his opponent.
Murray 3-6 4-5* FedererThe Scot is frustrated, but he bosses a couple of rallies to get to 30-15. He embarrassingly miscues a forehand on the next, which was your typical park-tennis stuff, but he holds after Federer hooks a shot into the tramlines. Federer has yet to offer Murray a break point. Will that change in the next game? It needs to...
Murray *3-6 4-6 FedererSET! Federer is furious that a Murray lob isn't called out, and the Scot fires down a forehand winner for 0-15. That's only gone and pumped the Swiss up, and he aggressively puts away a forehand at the net. A 23-shot rally is fiercely fought, but Federer prevails, only to send a backhand long. We are at 30-30. What next? It's SET point to Federer! He missed with an attempted backhand winner after some fine work from the Swiss, and Federer is two sets up after Murray goes long with a forehand pass. It's an uphill task from here...
Murray 3-6 4-6 1-0* FedererThat last game could prove pivotal. Murray had an opening. He needs to start well in this third set, but can he? The answer is no. Federer takes two of the first three points before directing a passing shot to the backhand side of the Scot. It's two break points to Federer, but Murray saves them both! Another break point is saved with a drive volley into the corner, and the Wimbledon champions shows supreme fighting qualities to seal the game with a brave forehand from the back of the court.
Murray *3-6 4-6 1-1 FedererMurray takes the opening point, but Federer powers his way to the next two. Another big shot from the baseline brings up two game points, before an ace levels the set.
Murray 3-6 4-6 2-1* FedererMurray plays two fantastic shots to Federer's backhand to take control of the game, but two equally glaring errors help the Swiss to 30-30. The 17-time Grand Slam winner has break point after forcing Murray onto the defensive, but Murray plays an incredibly aggressive point to earn deuce. Murray is digging so deep, and two big serves keep him ahead. He just needs to find some success on the Federer serve, which is easier said than done.
Murray *3-6 4-6 2-2 FedererFederer sweeps to 30-0, and a serve out wide brings up three game points. It's all so easy. Murray then goes wide with a forehand, and in next to no time, the pressure is back on the Scot.
Murray 3-6 4-6 3-2* FedererThe early warning signs are there when Murray goes long, but back-to-back volleys and a big first serve earn two game points. Federer saves one, but he can't save a second as Murray pulls out a a solid serve out wide.
Murray *3-6 4-6 3-3 FedererIt's a change of shirt for Murray, but can it bring a change in fortune? Maybe. Federer frames a forehand to make it 15-15, but maybe not. Two super serves bring two easy put-aways, and more aggressive play forces Murray to go long. Federer has conceded one break point in his last five-and-a-half sets.
Murray 3-6 4-6 4-3* FedererFederer is all over the net at 15-15, but Murray offers a fantastic response, directing the ball to the left of the Swiss who is forced to net. It gives him the momentum, and he imposes himself on the game to take a 4-3 lead.
Murray *3-6 4-6 4-4 FedererThis is so good from Federer. A smash and a backhand volley comfortably takes him to 30-0, before he sneaks into court to convert another. However, Murray rifles a return winner past the Swiss, before nearly obliterating the ball with a smash at the net, which was also directed at Federer. Cheeky. It was, perhaps, a bad move as Federer responds with a big forehand to repel the threat from the Scot.
Murray 3-6 4-6 4-5* FedererBREAK! Murray caresses a volley over the net to take the early advantage, but a 27th unforced error from Murray gives him 15-15. What have we just seen there?! Federer stretches to retrieve a drop-shot and the ball flies over the head of Murray. It's a miraculous get, one that Murray can't believe. Dangers signs for the Scot, and it gets worse when he goes long from the baseline. Two break points for Federer! Ouch. Murray nets, and that could be that.
Murray *3-6 4-6 5-5 FedererBREAK! Murray must break here or else he is out. What can he do? Federer miss-hits a backhand into the net, before Federer goes wide with a forehand. The Swiss comes roaring back with a big serve down the middle, but Murray has two break points after a fantastic return! Finally, but can he convert? YES! Federer saves the first, but after Federer floats a shot long, Murray has the break!
Murray 3-6 4-6 6-5* FedererA big forehand winner gives Murray the opening point, but a poor slice into the net levels things for Federer. However, two aggressive baseline shots bring up two game points for the Scot, which is soon sealed with a first serve.
Murray *3-6 4-6 6-6 FedererBack to normal for Federer, who puts away a forehand at the net, and Murray can't take advantage after moving the Swiss around the court on the next point. A first serve out wide is too hot to handle for Murray, and we are heading into a tie-break after an easy hold from the Swiss.
Murray 3-6 4-6 6-6 (2-4)* FedererA super one-two from Murray gets him off to a good start, but he misses out after trying to take on a Federer second serve. A stunning ace out wide takes the Swiss into a 2-1 advantage, but Murray steps in to smash his way to 2-2. Federer has the mini-break when Murray hits a backhand long, and that is immense from the Swiss! He claws several Murray shots back over the net, forcing Murray to wilt and put the ball long.
Murray *3-6 4-6 6-6 (6-6) FedererFederer fires down a big serve out wide to move to 5-2. He's on the brink now. However, Murray finds a first serve to get back to 5-3, before driving a forehand down the line. Federer has two serves for the match. So close from Murray, but he misses with a backhand return and Federer has TWO MATCH POINTS! It's so tense, but Murray saves the first, connecting with a forehand cross-court. Can he save a second match point? YES HE CAN! A backhand from Federer goes wide. Remarkable.
Murray 3-6 4-6 7-6 (8-6) FedererWhat a winner from Murray! He catches the line with a forehand and he has SET POINT! Can Murray salvage this set? YES HE CAN! WOW!!! Federer goes long and we are heading into a fourth set.
11.00amLadies and gentleman, and kids that should be at school, we have one fired-up Scot.
Murray *3-6 4-6 7-6 0-1 FedererThat was incredible stuff, but Murray needs to stay on top of this. The errors are coming from Federer now, and he sends two horrendous shots off target. However, Murray does the same when attempting a forehand passing shot for 15-40! It's 30-30, and it's Federer who gets to game point when Murray goes wide. The game is sealed with a drop-shot and Federer needed that.
11.22amTrouble for Murray. Federer flashes two forehands past the Scot for 0-30, and a poor forehand into the net gives Federer three break points. The first is saved with a delicate drop-shot over the net, before Federer dumps a forehand into the net on the second. Can Murray save a third? He can, you know! What a shot from the baseline. It's deuce, which quickly becomes advantage to Murray with a seventh ace. Federer's still fighting though, and he earns another break point after the Scot goes wide, but Murray saves again! This game has elapsed 10 minutes with Murray missing three game points. It's a marathon game, and now Federer has break point after a forehand catches the line, but it's saved for a fifth time when Murray converts a smash! Incredible. I don't believe this. An ace brings up game point, but Murray fails to take advantage at the net!
Murray 3-6 4-6 7-6 1-1* FedererWe are still going in this second game of the fourth set after five break points for Federer and five game points for Murray. What next? Murray misses with an attempted backhand pass and it's a sixth chance for Federer. Will this mammoth game come to an end? No it won't! Murray nails a drop-volley which Federer puts wide. It's the 10th deuce and we are at 18 minutes for this game. Murray lets fly from the baseline for game point, and he's held serve! Finally! Murray connects with a passing shot into the open court. They will write stories about that game.
Murray *3-6 4-6 7-6 1-2 FedererMurray's back got a severe going-over in that last game, and it is perhaps no surprise that Federer holds to love. This could be a tough service game for Murray.
Murray 3-6 4-6 7-6 2-2* FedererThere's not a whole lot on that first serve from Murray, but he takes the point. Federer sends a second-serve return long to give Murray 30-0, but there's a grimace from the Scot. Federer sprays two more returns long and the Scot holds to love, but it's going to take an herculean effort from here.
Murray *3-6 4-6 7-6 2-3 FedererMurray makes good ground to flick a backhand past Federer for 15-15, but a stiff-looking return from the Scot finds the net. A forehand winner and an ace earn the Swiss the game.
11.44amWe move into the fourth hour of this gripping encounter, and a couple of timely first serves earn Murray 30-0. Federer responds with a wonderfully-whipped forehand that catches the line, before Murray misses with a backhand pass. This is a crucial time for the Scot, but he achieves game point with a deep forehand. That's quickly taken away when Federer crunches a forehand return winner for deuce. Federer is pulling Murray all around the court, and he earns break point when Murray can't direct a backhand smash over the net, but it's saved with a brave volley at the net. Here we go again?
Murray 3-6 4-6 7-6 3-3* FedererMurray saves us from another ridiculously long game with two dominant points from the back of the court. He is hanging in there, but I have no idea how.
Murray *3-6 4-6 7-6 3-4 FedererFederer eases to a 40-0 advantage, and Murray is beginning to look weary. The Scot gets back to 40-30, but Federer retains his composure to put away a challenging smash.
Murray 3-6 4-6 7-6 3-5* FedererBREAK! Murray's back is causing him trouble, and the pain is made worse when two forehand errors hand 0-30 to Federer. It soon becomes 0-40 when Murray plants another forehand long of the baseline. This could be the moment. Murray connects with two first serves, but Federer breaks! Murray does brilliantly to remain in the rally for as long as he did, but Federer eventually flicks the ball into the open court.
Murray 3-6 4-6 7-6 3-6 FedererMATCH! Murray is still fighting, and a trademark forehand winner finds the line. The Scot produces the goods on the next point too, flicking a forehand out of the reach of Federer. The Swiss responds with an authoritative point, before getting to 30-30 with an excellent second serve. Will it be break point or match point? It's match point, for a third time for Federer, after Murray goes long with a return. That's it! An ace from Federer, and the Swiss is through to the semi-finals.
12.00pmI can't quite do that match justice with a few words, but it was everything that it promised to be. Federer was terrific, relentless, even mesmeric at times, while Murray displayed all of the fight that we haven't seen since his back surgery. The Scot deserves so much credit for salvaging that third set from the brink of defeat, but Federer deserved this triumph.
12.01pmThe Swiss maestro will attempt to continue his quest for an 18th Grand Slam when he faces Rafael Nadal on Friday. I don't think anyone is going to want to miss that.
12.03pmThat will be all from Sports Mole for this match. We thank you for joining us for this incredible match, and we invite you to return over the next few days for the closing stages of what has been an absorbing Australian Open. Goodbye for now.