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Unai Emery’s current and former clubs cruised through on Wednesday with home second-leg wins.
Villa beat Club Brugge 3-0 to secure a 6-1 aggregate win, with Arsenal’s 2-2 draw with PSV giving Mikel Arteta’s side a 9-3 two-legged victory.
Paris St-Germain beat Premier League leaders Liverpool on penalties on Tuesday after a 1-1 aggregate draw.
Real Madrid edged Atletico on penalties to knock them out of the Champions League for the fifth time in 11 years.
The other quarter-final ties see Inter Milan play Bayern Munich and Borussia Dortmund face Barcelona.
Highlights of every Champions League game are available on BBC iPlayer and the BBC Sport website and app.
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