Arsenal’s Champions League run came to an end as Joshua Kimmich’s header earned Bayern Munich a narrow 1-0 win in the second leg of the Champions League quarter-final tie.

It was all to play for heading to Munich, after a 2-2 draw in north London a week ago, and there was still nothing to split them after a nervy hour.

Bayern had by that point hit the post twice, though, through Leon Goretzka and Raphael Guerreiro, and it was the hosts who edged in front on the night and on aggregate.

Guerreiro got on the end of Leroy Sane’s ball across the face of goal, clipped it back into the middle himself and Kimmich timed his run perfectly to arrive on the scene and power a header past David Raya.

That left Arsenal with 30 minutes to find an equaliser to send it to extra-time, but Bayern saw the match out in comfortable fashion, as the Gunners failed to end their 15-year wait for a Champions League semi-final appearance.

The win also maintained England captain Harry Kane's chances of winning silverware in his debut season in Germany, the former Tottenham striker missing out on a Bundesliga title following Bayer Leverkusen's remarkable campaign.

Kane had a quiet evening after half a chance in the opening exchanges and it was Arsenal who enjoyed a good spell as they looked to take the lead in the tie.

Gabriel Martinelli flashed a shot wide before wiggling through a couple of challenges only to come up against the imposing presence of Bayern skipper Manuel Neuer in the hosts' goal.

At the other end, David Raya was called into action for the first time as he saved from Jamal Musiala following a speedy Bayern break.

Neuer's first meaningful action of the night saw him paw a deflected Martin Odegaard shot off target as he sprang up to prevent the ball running behind for a corner.

Martinelli then missed a great chance to open the scoring just after the half-hour, shooting straight at Neuer when picked out free in the Bayern box.

Bayern were fuming as they looked to catch Arsenal out after Bukayo Saka was down needing treatment and Mikel Arteta gathered his players on the touchline only for the winger to clamber to his feet.

A quick throw-in with all of the Arsenal side distracted was instead pulled back by referee Danny Makkelie, much to the chagrin of the home fans.

Bayern were second best for the majority of a largely passive first 45 minutes for the hosts, but straight after the restart they were on it, hitting the crossbar through a Leon Goretzka header before Raphael Guerreiro's follow-up deflected against the post.

Arsenal were slightly rattled and Gabriel Magalhaes passed the ball out of play for a corner following a breakdown in communication with Raya.

Arsenal survived the resulting set-piece but fell behind soon after, Kimmich flying past a slow-moving Martinelli to power Guerreiro's cross into the back of the net.

Arteta reacted almost immediately by turning to his bench, bringing on Gabriel Jesus and Leandro Trossard but Arsenal's race appeared to be run.

They struggled to create any chance of note in chasing the game, taking more and more risks at the back in doing so.

This may not have been a repeat of Arsenal's two previous visits to the Allianz Arena, both 5-1 defeats, but it showed Arsenal are still a step below Europe's elite.

Additional reporting by PA Sport.