In the first half, it looked like Bayern were just killing time until something more interesting happened. They were basically doing that thing where they hold their little brother at arm's length by the forehead while the little brother swings his arms and fists with all his might, trying to land a punch even though his arms are shorter than his big brother's. Arsenal worked their butts off, but Bayern were in another gear entirely, and never once looked threatened.
Then, the second half started. Arsenal looked a bit brighter, but Bayern took a second-half lead when Bastian Schweinsteiger scored in the 55th minute. It's all over now, right? WRONG BITCHES. Lukas Podolski promptly went the other way and scored, to make it 1-1 and make it very tasty indeed.
For the rest of the second half, Arsenal looked a ton better, as they worked and worked and caused Bayern to dive and dive and dive. Arsenal couldn't find the goal, though, and in the first minute of stoppage time, Divey McDivealot dove like a diving diver and "earned" Bayern a penalty. What happened next? FABIANSKI HAPPENED.
But in the end, Arsenal's vastly improved second half wasn't enough, as that was it for the action, and the game ended 1-1. So Arsenal lose 3-1 on aggregate, and thus endeth the Champions League for another season.
Do not believe the narrative that you'll no doubt start hearing again at top volume; Arsenal didn't collapse. Arsenal played very well today; for the first half, at least, Bayern played better, and the 2-0 from the first leg was just too much to overcome. If Arsenal play like this in the Premier League between now and May, they may well not lose again.