City and Real are regarded as favourites for the competition. It is the third successive season City have met Real in the knockout stages.
Arsenal, meanwhile, will face Bayern Munich.
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The first legs take place 9-10 April, with the second legs on 16-17 April.
Quarter-finals draw
Arsenal v Bayern Munich
Atletico Madrid v Dortmund
Paris St-Germain v Barcelona
Real Madrid v Manchester City
Semi-finals draw
Atletico Madrid or Borussia Dortmund v Paris St-Germain or Barcelona
Arsenal or Bayern Munich v Real Madrid or Manchester City