All the remaining games will be one-legged and behind closed doors, after the initial two-legged ties in March were postponed because of the coronavirus pandemic.
Lyon's England full-back Lucy Bronze told BBC Radio 5 Live: "With the new style of the competition - one game, winner takes all - anything can happen and there are a lot of strong teams.
"But we're all confident. We know if we play at our best we can beat any team out there."
Where is it taking place?
Bilbao and San Sebastian are hosting the conclusion of the competition, which will use a similar format to that seen in the men's Champions League and Europa League.
Bilbao's San Mames Stadium and San Sebastian's Anoeta Stadium are the two venues, with the latter staging the final on Sunday, 30 August.
There will not be crowds at the fixtures and all teams are having to adhere to strict safety protocols and Covid-19 testing.
Who is left in the competition?
Arsenal, Britain's only previous women's European champions in 2007, will meet French side Paris St-Germain on Saturday (19:00 BST).
Joe Montemurro's Gunners overcame Italian club Fiorentina and Slavia Prague of the Czech Republic in the last 32 and last 16 respectively earlier in the tournament.
Glasgow City are also through to the last eight, after edging past Danish side Brondby on penalties in November.
The Scottish league champions face a tough tie on Friday (17:00) against German side Wolfsburg, who have reached the European final four times since 2013, winning the title twice.
Meanwhile, Atletico Madrid will face their domestic rivals Barcelona on Friday, a match which pits Atletico's England forward Toni Duggan face her former club.
The other quarter-final is a meeting between holders Lyon and German giants Bayern Munich, which kicks off at 19:00 on Saturday.
Can Lyon be stopped? And what are the British teams' prospects?
Lyon are favourites to win a fifth successive Women's Champions League
Lyon are the clear favourites to retain the title, having won the past four finals.
They have been European champions a record six times and reached a further two finals, dominating the competition since 2010.
Their team includes the England quartet of Bronze, Nikita Parris, Alex Greenwood and Jodie Taylor, the latter having on 4 August.
If Lyon get past Bayern, they will face the winner of Arsenal and PSG's tie in the semi-finals on Wednesday.
The other half of the draw pits the winner of Glasgow City and Wolfsburg's game against the victor in the all-Spanish tie, on Tuesday.
Both British clubs have difficult draws and may find their hopes dampened by the fact some of their rivals have played more competitive football than them over the summer.
Asked which team will be the biggest threat to Lyon, Bronze said: "Wolfsburg. They're on the other side of the draw to us, so if we were to play them it would have to be in the final.
"They're a team we've played in the final before and they've got a really good squad. But you look at all the teams now and, not to be cliche, but they've all got something about them.
"They're all obviously good teams to get to the position that they are."