Cristiano Ronaldo's hat-trick helped Real Madrid to become the first team to reach seven consecutive Champions League semi-finals.
The Blancos, who won the competition for the second time in three campaigns in 2016, defeated Bayern Munich 4-2 on Tuesday to reach the last four with a 6-3 aggregate victory.
Robert Lewandowski's second-half penalty and a Sergio Ramos own goal either side of a Ronaldo effort took the match into extra-time at the Santiago Bernabeu.
Two more goals from Ronaldo - both of which looked offside upon replays - and a Marco Asensio strike catapulted Zinedine Zidane's men past their German opponents.
Real Madrid began their seven-season streak in 2010-11 when they reached the Champions League semi-finals for the first time in eight years.
Their resurrection as a European team to be feared has coincided with Spanish dominance on the continent. Barcelona have triumphed twice in six years while Atletico Madrid have reached two of the last three finals.
Madrid rivals Atletico joined Real in Friday's draw, with the matches taking place in the first and second weeks of May.
The Champions League final will take place in Gareth Bale's home country of Wales, at the Millennium Stadium in Cardiff.