Arsenal will face Atletico Madrid in the Europa League semi-finals, while Red Bull Salzburg meet Marseille.
Liverpool, five times champions themselves beat runaway Premier League leaders Manchester City 5-1 on aggregate to set up their meeting with Roma.
Real Madrid who advanced to the semi-final following a Cristiano Ronaldo penalty in stoppage time when Juventus were at the brink of what would have been the greatest comeback in Champions League history. I believe it comes down to the first leg. If Lewandowski and James Rodriguez can penetrate Madrid's defense in Munich, Bayern could have it sealed when they go to the Bernabeu.
Real Madrid have reached the semi-finals for the eighth successive season, and the 12-time winners are on the hunt to become the first side to lift the Champions League title in three consecutive seasons.
The Europa Leaguechampion will get direct entry into next season's Champions League.
The first legs will be on April 24 and 25 and the returns on May 1 and 2, while the final is scheduled for May 26 at the Olympic Stadium in Kiev, Ukraine.
Liverpool staff gathered at the Melwood training base to watch the draw together, with the club's Twitter account depicting the tense scenes moments before the balls were picked out of the bowl. "It's important to play a good game at Anfield, after which we have the slight advantage of playing the second leg at home - where we will have the great passion of our fans to push us on".
This is the fourth time in the past seven tournaments that the sides have met in the semi-final stages. The final will be played on May 16 in Lyon.
Jurgen Klopp's men produced two displays of guile and maturity to see off City in the all-English quarter-final. "It is possible. We need to be focused".
"I still talk to most of the players there".
Liverpool have five Champions League titles to their name, and they have a good chance to make it six in May. Liverpool is owned by Boston's boy, John Henry, so it will be fun and it will be nice to see Salah again.