Chelsea, last season's beaten finalists, defeated championship side Middlesbrough 2-0 at the Riverside stadium on Saturday thanks to first half goals from Romelu Lukaku and Hakim Ziyech.
Crystal Palace thumped Frank Lampard's Everton 4-0 at Selhurst Park on Sunday to make it into the last four of the world's oldest club competition.
Manchester City saw off Southampton 4-1 at the Saint Mary's stadium also on Sunday, with the likes of Raheem Sterling, Kevin De Bruyne, Phil Foden and Riyad Mahrez all getting on the score sheet.
Later on Sunday, Liverpool takes in a trip to Nottingham Forest and the winner of that tie will face Pep Guardiola's side in the next round.
The semi-final ties will be played at Wembley on the weekend of April 16-17.
Leicester City are the current holders of the competition, having beaten Chelsea 1-0 in last season's final.
FA Cup Semi-Final draw in full:
Chelsea V Crystal Palace
Man City V Nottingham Forest/Liverpool
