Defending champions Bayern Munich, who are looking to become the first team to win the Champions League twice in a row, will take on Manchester United in a high-voltage clash in the quarter-finals.
In an all-Spanish clash, former winners Barcelona were drawn against Atletico Madrid in the Champions League draw, which took place in Nyon, Switzerland, on Friday.
Bayern Munich won the Champions League last year, beating fellow Germans Borussia Dortmund 2-1 in the final, at the Wembley stadium in London.
Real Madrid will look for revenge when they take on Borussia Dortmund, having lost to the German club in last year's semi-finals.
Paris Saint-Germain were handed a tough draw against Chelsea.
Real Madrid have won the tournament a record nine times, while Bayern Munich have won the tournament five times.
For the second year in a row, Spain is the most represented country with three teams, followed by England (2), Germany (2) and France (1).
Unlike last year, one of Europe's Big Four is missing as Italy's AC Milan were eliminated from round 16.
The first legs will be played on April 1 and 2 April while the return will be on April 8 and 9.
Quarter-finals line up:
Barcelona vs Atletico Madrid
Real Madrid vs Borussia Dortmund
Paris Saint-Germain vs Chelsea
Manchester United vs Bayern Munich