Holders Chelsea will face 13-time winners Real Madrid in the quarter-finals of the Champions League.
Manchester City will play Atletico Madrid, while Liverpool tackle Benfica and Bayern Munich take on Villarreal.
In the semi-finals, the winner of the Chelsea v Real Madrid tie will face Atletico Madrid or Manchester City, while Benfica or Liverpool will play either Villarreal or Bayern Munich.
The two-leg quarter-finals take place on April 5-6 and April 12-13.
The first legs of the semi-finals will be on April 26-27, and the second legs on May 3-4.
The Stade de France in Paris will host the final on Saturday, May 28 after it was moved from St Petersburg after Russia’s invasion of Ukraine.
In the Europa League, West Ham will play Lyon in their first European quarter-final since 1981.
Rangers take on Portuguese side Braga, while Eintracht Frankfurt play Barcelona and RB Leipzig face Atalanta.
The draw means Chelsea face a reunion with their former manager Carlo Ancelotti, who won the Premier League and FA Cup double during a two-year spell with the Stamford Bridge club between 2009 and 2011.
The Italian is one of only three managers to win the Champions League three times, including with Real in 2014, and returned for a second spell at the Spanish giants last summer after leaving Everton.
Chelsea and Real also met at the semi-final stage last season, with Thomas Tuchel’s side winning 3-1 on aggregate before going on to beat Manchester City in the final.
The London club have never lost in five previous meetings with Real Madrid.
Champions League quarter-final draw
Chelsea v Real Madrid
Manchester City v Atletico Madrid
Villarreal v Bayern Munich
Benfica v Liverpool
Champions League semi-final draw
Manchester City or Atletico Madrid v Chelsea or Real Madrid
Benfica or Liverpool v Villarreal or Bayern Munich
Europa League quarter-final draw
RB Leipzig v Atalanta
Eintracht Frankfurt v Barcelona
West Ham v Lyon
Braga v Rangers
Europa League semi-final draw
RB Leipzig or Atalanta v Braga or Rangers
West Ham or Lyon v Eintracht Frankfurt or Barcelona