The three Premier League and three La Liga teams in the last eight avoided each other, with Manchester City up against Atletico Madrid, Liverpool taking on Benfica while Villarreal will play Bayern Munich.
There is the potential for teams from the same domestic division to face off In the semifinal draw, with the winner in the Chelsea/Real Madrid tie playing Manchester City or Atletico. Meanwhile, Benfica or Liverpool will face Villarreal or Bayern.
Real Madrid coach Carlo Ancelotti will return to former club Chelsea for the first leg and Thomas Tuchel described the challenge as a "tough one."
As things stand, Chelsea will not have any fans at either leg after UEFA said it would uphold EU sanctions against Russian owner Roman Abramovich who has had his assets frozen since announcing he was selling the club.
"The challenge cannot be higher," Tuchel told reporters on Friday. "Playing the second leg in the Bernabeu with spectators is a big challenge. We know what's coming, but there is a big excitement around this fixture.
"It's nice to avoid the English clubs, it's always nice to play European teams."
Asked about the prospect of having no Chelsea fans at either leg, Tuchel added: "In general I think this game changes so much with spectators so hopefully we find a solution and I'm pretty sure everyone at the club, the board, will fight for a chance."
"Hopefully we make it happen somehow."
Real Madrid, beaten by Chelsea in last season's semifinals, are 10 points clear at the top of LaLiga while Tuchel's side are third in the Premier League.
Liverpool will consider a clash with Benfica as the best option from the draw and they could even face Premier League title rivals Manchester City in the final in Paris.
City will have to get past the considerable challenge of Atletico Madrid though -- a clash that will be a fascinating contrast in styles and a tactical battle between Pep Guardiola and Diego Simeone.
It will be the first meeting between the two clubs.
Atletico coach Diego Simeone said of being drawn to play City: "Above all a great admiration for [Pep] Guardiola, and for the work he's been doing at City in recent years, which is shown game after game. After that, it's a difficult competition, they are great ties between all the teams. We'll have time to assess the game, now we focus on our game against Rayo Vallecano, that's all I have in my head."
The fixtures will be confirmed shortly, but as both Madrid teams have been drawn at home in the second leg of the quarterfinals, it is expected one tie will be reversed. As Atletico Madrid qualified as Spanish champions, their tie will remain unaltered, while Real Madrid's game against Chelsea should be reversed and the second leg held at Stamford Bridge. This also happened in 2019 when both Manchester City and United were drawn at home, with United's tie switched around.
Quarterfinal first legs will take place on April 5 and 6, with the second legs on April 12 and 13.
The semifinal first legs follow on April 26 and 27, with the return legs on May 3 and 4.
Champions League quarterfinal draw:
Chelsea vs. Real Madrid
Manchester City vs. Atletico Madrid
Villarreal vs. Bayern Munich
Liverpool vs. Benfica
Champions League semifinal draw:
Manchester City or Atletico Madrid vs. Chelsea or Real Madrid
Liverpool or Benfica vs. Villarreal or Bayern Munich