Trailing 3-1 from the first leg in London, the Gunners had to win by three clear goals to qualify for the next round outright.
As it was, Arsene Wenger's side almost pulled off the unthinkable. An early strike from Olivier Giroud provided the visitors with belief and they set up a grandstand finish when Laurent Koscielny scored a late header.
It wasn't to be though and the hosting Germans held out to book their place in the last eight of the tournament.
To find out how the match unfolded, you can read our minute-by-minute commentary below.
Evening all! Right, let's start with a question. Who honestly believes that Arsenal have a chance of progressing through to the quarters-finals of the Champions League tonight? Anybody? Didn't think so.
But hold your horses - this is football after all. As we've seen so often with this sport, literally anything can happen. For example, who thought that Chelsea would win this competition last year? With 90 minutes gone, who felt that Manchester City were going to lift the Premier League title? See, don't despair Arsenal fans. Clutching at straws? Probably!
So, the reports from earlier today that Santi Cazorla and Theo Walcott were going to be rested have proved to be not true - they both start. Also included in the team is full-back Kieran Gibbs, which has meant that Thomas Vermaelen has dropped down to the bench. Lukas Fabianski will keep goal, with Wojciech Szczesny having "mentally affected" by the number of matches that he has played recently.
Well, for a team that is missing three key players, that is still a very, very strong looking lineup. Arjen Robben has overcome a calf complaint to start, while Luiz Gustavo has come into the centre of midfield to replace Schweinsteiger. Elsewhere, Mario Mandzukic, who scored during the first leg, has been given the lone striker's role.
What has Arsene Wenger had to say about the situation that his team is in then? Well as you'd expect, he has refused to rule out his side advancing.
"It is not mission impossible," Wenger told the club's official website. "It can be done, but first of all you need 100% commitment, attitude and things to go your way. But usually football goes your way when you have the right attitude.
"There is a kind of [feeling of] 'let's really play with freedom'. Let's start strong. We have to create doubt in their mind and you only do that if you have a real go."
Like most, Wenger's opposite number Jupp Heynckes is refusing to say that the tie is over - well at least in public anyway!
"We had a very good day against Arsenal [in the first leg]; the first half was excellent, the second quite good," he told reporters. "But Arsenal are still Arsenal. For many years they have played great football. I remember [last season] Arsenal lost the first leg 4-0 to Milan but then won 3-0 at home, nearly scoring a fourth goal.
"We are not paying attention to the hype around us. People are saying we are the best team in Europe; that does not affect us.
"There are so many strong teams in Europe and to reach the final you always need a little luck. So my team remains calm and down to earth. We have a long way to go."
Let's take a look at the enormity of the task that is ahead of Arsenal shall we? Just to cheer everyone up! No team has ever overturned this sort of deficit when they have lost the home leg. In fact, only two teams in the history of the competition have advanced after losing the home leg. Gulp!
Having said all that, one of those teams to progress after losing at home was Inter Milan. And who did they knock out? Bayern Munich! The Germans won the first leg in the San Siro 1-0, but ended up losing in the Allianz 3-2, meaning that Inter went through on away goals. Granted Arsenal have a lot more work to do than that, but it is something to hold on to at least.
From looking at Twitter, it seems that most Arsenal fans are fearing the worst tonight. A number of them are tipping a heavy defeat. Perhaps most supporters of the Gunners would simply take their side winning the match 1-0 or 2-1. Okay they wouldn't progress, but at least they will give their fans something to celebrate.
Former Arsenal goalkeeper Jens Lehmann has just been talking to Sky Sports News. He is not exactly confident that his ex-employers have much chance tonight.
"We will see if Bayern are too complacent. That could be Arsenal's only chance. No game starts with zero chances. You never know."
There was heck of a pause before he answered the question - almost like he didn't truly believe what he was saying!
Right then, the players are slowly beginning to filter out into the tunnel area. Have to say, the few Bayern players that are standing there don't look to be nervous at all - but then why would they? They know that they are more than capable of winning this match.
Before we get started, another ex-Arsenal keeper - John Lukic - has been talking to BBC Sport. Here is what he has had to say about this match:
"Arsenal should go into the game thinking they can do this. The overriding thing is that they can't afford to concede a goal. A clean sheet gives them a chance.
"Given Bayern's form this season and looking where they are in the German league it looks unlikely Arsenal can get a result, but that being said football is a funny business and anything can happen.
"On their night Arsenal is a match for anybody and can beat anybody. If they turn up tonight it might be an interesting game, but if they concede, that kills the tie."
Here come the players. It's a great atmosphere inside the Allianz Arena. It really looks to be a cracking venue to play football in. Not long now until we are off and running.
Now hang on a minute, this wasn't meant to happen! Arsenal are back in this tie. Santi Cazorla and Tomas Rosicky link to free Walcott inside the penalty area. He powers the ball low across the goal for Olivier Giroud, who gleefully lifts the ball into the net from close range. The Allianz Arena is stunned into silence. I'm stunned. Everybody is stunned! Game on.
It's vitally important that Arsenal maintain their focus defensively. If they concede, that is pretty much game over. It doesn't seem like they have altered from the recent North London derby though because they are still playing with such a high line. It's risky, but it may work.
CHANCE! The first escape as far as Arsenal are concerned. They fail to clear a corner from Toni Kroos and the ball eventually works its to Gustavo on the edge of the box. He takes an instant shot, but it goes wildly over the crossbar. The midfielder had enough time to take a touch there.
The Gunners seem to be getting support from all over the globe at the moment. England spin-bowler Monty Panesar, who is in New Zealand, has just tweeted this:
What has been done to the Allianz Arena pitch? In the first 15 minutes so many players have slipped over. I've heard of making the pitch wet to help with passing football, but this is ridiculous. It's more like a swimming pool!
Here is something that may interest Arsenal fans from statisticians Infostrada:
"Giroud's third minute goal was the fastest Champions League goal for Arsenal since Freddie Ljungberg scored in the second minute against Ajax in Sep 2005."
Since Arsenal opened the scoring, very little has happened. To be honest, that will suit the Londoners. Scoring another goal would be great, obviously, but if they can keep it this way until half-time, a few doubts may creep into Bayern minds. The crowd is already quieter than normal.
SAVE! Do Arsenal want to get through? First Aaron Ramsey gives the ball away on the edge of his own area and when it is retrieved, Mikel Arteta does the same thing. Kross looks to punish the Spaniard by shooting from 20 yards out, but Fabianski does well to hold his low effort.
CHANCE! Pretty much every problem Arsenal are having at the moment is being caused by themselves. This time Per Mertesacker scuffs a clearance straight to Thomas Muller, who then beats the Arsenal defender. The angle is always against the attacker though and he fires the ball into the side netting. Perhaps he should have looked to cross there.
Brilliant stuff from Walcott - his pace is so dangerous. He picks up the ball on the right and runs at David Alaba, who backtracks. That allows Walcott to drill in a cross, which is just too speedy for Giroud and the Frenchman cannot make any contact. If he had, he would surely have scored.
Arsenal are really struggling to keep hold of the ball. Every time they pick up possession, Bayern are hunting in packs and are forcing their opponents to rush their passes. More often than not they go astray and the Germans regain the ball. It's something that will need change if the Gunners are going to somehow get through.
There's some potential bad news for Arsenal as Giroud is down following a challenge with Daniel van Buyten. He looks to be in a lot of pain. The pair appeared to clash knees and Giroud immediately put his hand up for medical help.
The French striker is up and is now back with us, but he is moving extremely gingerly. He will probably get some treatment at half-time and will see how it goes from there. He's given Arsenal a focal point this evening so it would be a shame if he had to go off.
BOOKING! The first yellow of the evening goes to Arsenal's Gibbs. The full-back is not happy with it, but a replay shows that he got very little of the ball once he went into a sliding challenge with Robben. A deserved caution.
If you had offered Arsene Wenger, the Arsenal players and all their supporters this scenario before the match, each of them would have snapped your hand off. They are 1-0 up and although there is still a lot of work to be done, they have a better chance of getting through than what they started with tonight. You can't really have asked for much more.
The best way to describe that first half from Bayern is very un-Bayern like! There was no zip about their play and they have not caused the Arsenal defence and goalkeeper many problems at all. In fact, every chance Bayern have had has come from an Arsenal error. The crowd is also strangely quiet, which probably isn't helping.
Although according to a Bayern fan on Twitter, the lack of atmosphere has nothing to do with the scoreline. Here is what Felix Wagner has put it down to:
"The reason for the lack of atmosphere is the fact that the active supporters can't get behind the goal in ucl - not the score line.
"Same thing when they thrashed Lille or in any other UCL game this season - in case u watch sky uk and wonder."
So, what do Arsenal need to do in the second half? Well, score two goals obviously! But to make that happen they must keep the ball much better. At times they were far too wasteful in possession. The other (worrying) factor is that you'd have to expect a reaction from Bayern after the restart. They won't have played much worse than that all season.
CHANCE! Did Arsenal not learn from the first leg that they cannot give Kroos the room to shoot from distance. The German midfielder almost punishes them with a swerving shot from 25 yards out that has Fabianski well beaten. Thankfully for Arsenal, the ball whistles inches wide of the target.
The Arsenal midfield really has given the ball away far too frequently tonight. Arteta, Ramsey and Rosicky have all been guilty on numerous occasions. There's no way that the Gunners will score two more goals if this continues. It also increases the chances of Bayern finding the net.
What an earth is Giroud thinking? He chests the ball down 35 yards from goal and decides to try his luck from there. You've guessed it, the ball flies high, wide and not very handsome. What's worse, Arsenal had committed five men forward to that attack. His teammates and Wenger are not happy with him. What a waste.
BOOKING! It's 1-1 in terms of bookings as Bayern skipper Lahm sees yellow for pulling down Cazorla, who was looking to mount an attack. The full-back knew exactly what he was doing there and it is one of those cautions that you take for the team.
BOOKING! The most blatant yellow card you are ever likely to see for Rosicky. He gets involved in a race with Robben and there is only ever going to be one winner there. Rosicky knows that and decides to trip up the Dutch winger in full flight.
CHANCE! Bayern go very, very close to sealing their place in the next round. Lahm picks out Gustavo on the edge of the area and instead of opting for power, the midfielder curls the ball goalwards. It looks to be heading into the bottom corner, but it skips just wide of the target. Nervous times for Arsenal.
SAVE! Fabianski has just kept Arsenal in the Champions League...for now! A back-heal from Muller frees Robben, who is through on goal. Having got into the area, he goes for a chip, but the Polish keeper sticks up hand and pushes clear the danger. Arsenal are on very thin ice right now.
SUBSTITUTIONS: First switches for Arsenal as the disappointing Ramsey and Walcott come off. Why oh why has Walcott been taken off? He was Arsenal's main threat! Anyway, Alex Oxlade-Chamberlain and Gervinho come on in their places. Bayern also make an alteration as Mandzukic is replaced by Mario Gomez.
BOOKING! What a silly yellow card for Giroud to pick up. He is adjudged to have handled the ball and instead of accepting the decision, he decides to smash it into the advertising hoardings. You'd expect that from a five-year-old!
Half a chance for Giroud goes a begging. Jenkinson drills in a low shot for the striker, who loses his balance as he takes a touch. With his back to goal, he doesn't know whether to shoot or pass to Cazorla and eventually Dante sticks a foot in to clear. Had he been more decisive, Arsenal would have had a real opportunity.
CHANCE! Gervinho is not overly popular with Arsenal fans but he could have made himself a real hero just now. Cazorla picks him out inside the area with a low pass. His touch is brilliant and he then dances past Van Buyten. Out comes Neuer and Gervinho beats him with a low shot but unfortunately the ball skids just wide of the target.
BOOKING! Another foul on Robben and another booking for Arsenal. On this occasion it is Mertesacker who blocks off the former Chelsea winger and he is deservedly cautioned.
SUBSTITUTION: A sign that Bayern are ready to shut up shop as the attack-minded Kroos, who had a bit of a stinker to be fair, is replaced by Ukrainian Anatoliy Tymoschuk. He is much more of a defensive midfielder.
BOOKINGS! The referee has gone a little card happy for some reason. Bayern's Martinez is the man that sees yellow following a challenge with Rosicky. It's a crucial card for the Germans because Martinez will miss the next match if they progress. Moments later, Cazorla is booked for Arsenal for fouling Van Buyten. This stop-start stuff suits Bayern at the moment.
Wow! Just wow. Arsenal are just one goal away from the quarter-finals. It's an unlikely source that finds the net as well. Laurent Koscielny rises highest inside the area to meet a corner and he powers a downward header into the net - Neuer had no chance. What an ending we have in store. Brilliant from Arsenal. Who saw this coming?
BOOKING! Gomez joins the increasing list of players to be yellow carded as he hauls down Rosicky. It has given Arsenal a free kick just inside the Bayern half...but it squirms out for a goal kick. A waste from Arteta.
What is Arteta doing? For no reason he hauls down Martinez inside the Bayern half and takes all the pressure off the home team. That is so silly. His side have one minute left.
They gave absolutely everything, but Arsenal ultimately fell one goal short of the holy grail. The damage was done during the first leg but at least supporters of the Gunners can be proud of what they have seen tonight.
That's all we have time for from the Allianz Arena. Thanks for joining us in what was almost an amazing night for Arsenal Football Club. Until next time, goodbye.
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