Fran Kirby scored twice as Chelsea won through to meet Barcelona in the final.
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Chelsea are through to their first ever UEFA Women's Champions League final after defeating Bayern München 4-1 and 5-3 on aggregate.
Match in brief
Chelsea and Bayern had demonstrated the ample threats they posed to each other in the first leg, and Fran Kirby needed just 11 minutes to open the scoring in the return, combining slickly with Sam Kerr before clipping her side in front.
Sarah Zadrazil then notched her first ever Women's Champions League goal with a stunning long-range strike to level, before Ji So-yun replied from distance to leave extra time looming until the closing moments.
Pernille Harder put Chelsea ahead with a deft 84th-minute header, inspiring a frantic, thrilling finale that included a goal-line clearance from Blues captain Magdalena Eriksson, back from an injury that ruled her out of the first leg, and a near-miss from Kerr when clean through.
Kirby had the final say, slotting in after a counter-attack with Laura Benkarth out of position as Bayern battled for the goal that would have sent them through.
Key player: Ji So-yun
Among a team of players full of resilience, determination and class, Ji's was a quieter heroism, the midfielder keeping her side ticking over by looking after the ball, buying breathing room for her team-mates and moving possession beautifully. Her performance was encapsulated by the composure and quick-thinking with which she scored on the stroke of half-time, bringing Chelsea level in the tie with immaculate timing.
Emma Hayes, Chelsea coach: "We've been through a lot together. I've been here nine years – it's not just happened and it's been a long time coming. I'm going to have a nice singsong and cry all the way home because I'm so happy."
Pernille Harder, Chelsea forward: "I feel amazing. This is why we play football, winning like this. We were 2-1 down and we just put in unbelievable work, the whole team. We believed from the first minute and put in a great performance."
Jens Scheuer, Bayern coach: "The disappointment is huge. Chelsea weren't the better team in the two games but they were more effective. 4-1 is not deserved for us, especially after the score was 1-1, when we had good opportunities to take the lead ourselves. We still had good chances in the second half and even at 3-1 we still had chances that were stopped on the line."
• Chelsea's win was their first in their six UEFA Women's Champions League semi-final games, the Blues having previously lost four and drawn one.
• Chelsea have scored at least once in every competitive match since an FA Women's Cup tie with Manchester City on 21 April 2019.
• Chelsea have only failed to score once in their last 25 UEFA Women's Champions League matches.
• Before this game, Bayern had won all seven of their games in Europe this season.
Chelsea: Berger; Carter, Bright, Eriksson, Charles; Leupolz (Cuthbert 88), Ingle, Ji; Kirby, Harder (Spence 90+2), Kerr
Bayern: Benkarth; Ilestedt (Laudehr 87), Hegering, Glas; Beerensteyn, Zadrazil, Magull, Schüller (Dallmann 61), Simon (Wenninger 77); Bühl, Lohmann (Asseyi 77)
The final is at Gamla Ullevi, Gothenburg, on 16 May against Barcelona.