Liverpool will play Roma in the Champions League semi-finals, with Bayern Munich facing Real Madrid.
The Reds, who beat Manchester City 5-1 on aggregate in the last round, will host Roma on Tuesday, 24 April with the return leg on Wednesday, 2 May.
Arsenal will face Atletico Madrid in the Europa League semi-finals, while Red Bull Salzburg meet Marseille.
The Gunners will play the first leg at home on Thursday, 26 April, with the second leg a week later on 3 May.
The Europa League final will be in Lyon, France on Wednesday, 16 May, with the winner guaranteed a place in next season’s Champions League.
The Champions League final will be held in Kiev, Ukraine on Saturday, 26 May.
Liverpool, Champions League winners in 2005, have not faced Roma in a competitive match since March 2002.
The Reds’ top scorer Mohamed Salah will face the club he left for £34m in the summer.
Roma are fourth in Serie A – 21 points behind leaders Juventus.
They staged a remarkable comeback to beat Barcelona 3-0 on Wednesday and win their quarter-final on away goals after a 4-4 aggregate draw.