The round of 16 second leg tie between the two sides ended with City earning a 2-1 win (4-2 aggregate).
Raheem Sterling scored the opener for City, before Karim Benzema equalized for Real. Gabriel Jesus scored the winner.
Meanwhile, Juventus were knocked out by Lyon.
Here are the records broken.
Raphael Varane was robbed off the ball by Gabriel Jesus about 10 yards out by the byline. The Brazilian squared the ball for Raheem Sterling, who fired home the opener.
Karim Benzema equalized for the hosts in the 28th minute with a header.
The game got open with both sides getting chances, however, Jesus scored the winner after another Varane error at the back.
As per Opta, Jesus is now just the second player to score in both legs of a Champions League knockout tie against Real Madrid for an English side, after Ruud van Nistelrooy in 2002-03.
Benzema has scored five goals in his last six appearances in the Champions League knockout stages.
The Frenchman has raced to 65 career Champions League goals (fourth-highest).
Sterling is now just the sixth different Englishman to score 20 Champions League goals.
Wayne Rooney (24y 157d) managed to reach this total at a younger age than Sterling (25y 243d).
Sterling registered his 100th goal in all competitions for Manchester City.
He is now the first Englishman to reach three figures for the club since Dennis Tueart in 1981.
Cristiano Ronaldo, who scored a brace, has raced to 130 career Champions League goals.
Ronaldo has now scored 20 goals in his last 13 home Champions League knockout matches.
In total, he has scored 67 goals in the knock-out stages.
Ronaldo has ended the 2019-20 season with 38 goals across competitions.
Real Madrid manager Zinedine Zidane has been eliminated from a Champions League knockout tie for the first time. He was earlier victorious in the previous 12 games. Zidane has won just two of his seven, Champions League games against English teams.
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