Arsenal made a bitterly disappointing exit from the Champions League as they were beaten by Bayern Munich in a euphoric atmosphere at Allianz Arena.

Joshua Kimmich's powerful 63rd-minute header from Raphael Guerreiro's cross was enough to send the Germans through to the semi-finals 3-2 on aggregate after the two teams had drawn 2-2 in London in the first leg.

Despite being held at Emirates Stadium, Arsenal were confident of advancing against a Bayern Munich side who had endured a poor domestic season and were without key players Serge Gnabry and Kingsley Coman because of injury.

In a tight and cagey second leg, watched by Arsenal owner Stan Kroenke, Gabriel Martinelli had the best chance of the first half for the Gunners but shot straight at Manuel Neuer after Jamal Musiala had forced David Raya into a full-stretch save at the other end.

While Harry Kane had just nine touches in the opening 45 minutes, Neuer was forced into another save by Martin Odegaard's deflected attempt, which had the long-serving Bayern Munich keeper scrambling across his line.

With so much at stake for both teams, it was perhaps understandable chances were in limited supply but the second half was a livelier affair with Leon Goretzka heading against the post before Guerreiro's follow up was scrambled away by Raya, via the post.

But Kimmich's attacking header proved decisive and ensured Arsenal's wait to win the Champions League for the first time goes on.

Bayern will meet Real Madrid in the semi-finals after the record 14-time winners knocked out Manchester City on penalties.

"It's been a tough season for us," said England captain Kane, who scored in the first leg at Emirates Stadium.

"To reach the semi-finals is a great achievement for us and we can enjoy it. The expectation here is to try and win the Champions League."