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So, how many times have they actually won the competition? Goal brings you the full list of titles and more.
Real Madrid have won the European Cup (now Champions League) on 13 occasions, making the Spanish giants the most successful team in the competition's history.
Their first-ever European Cup triumph came in the 1955-56 season and it was the beginning of a record run whereby they won the tournament for five seasons in a row.
Having been the dominant force in European football during the 1950s, and to a lesser extent in the 1960s, Madrid had to wait until the late-1990s before they were once again at the top.
They had to wait a remarkable 32 years before they could get their hands on the Champions League crown, finally ending the drought in 1998 under the guidance of Jupp Heynckes.
Carlo Ancelotti famouslydelivered 'La Decima'- Real Madrid's 10th Champions League title - in 2013-14 before Zinedine Zidane led them to three Champions Leagues in a row from 2015-16 to 2017-18.
You can see the full list of Real Madrid's European Cup and Champions League wins in the table below.
Key: * 'La Decima' | AET - after extra time | P - game won on penalties.
In 2018, Zidane became the first and only Real Madrid head coach to win three Champions Leagues, doing what could not be achieved by iconic figures such as Vicente Del Bosque and Miguel Munoz.
As well as their 13 successful final appearances, the club have competed in three further finals - coming out on the losing side in 1962 (against Benfica), 1964 (against Inter) and 1981 (against Liverpool).
The closest team to Real Madrid in terms of success in the Champions League is AC Milan, with seven titles, followed by Bayern Munich and Liverpool, with six titles each.
Madrid's perennial Clasico rivals Barcelona lag well behind with five Champions Leagues in their trophy cabinet, though they have enjoyed similar levels of success in the post-1992 'Champions League era'.
Real Madrid have a genuine version of the Champions League trophy thanks to an old rule that was in place which allowed teams to keep the silverware if they won it five times in total or three times in a row.
An exclusive club of teams has won the trophy for themselves, with Bayern Munich, Barcelona, Liverpool and AC Milan joining Los Blancos.
The rule was scrapped from 2009 on and nowadays clubs are rewarded with a replica trophy, with UEFA keeping the original.
*As of the 2019-20 season.
While the European Cup / Champions League has been Real Madrid's favoured competition, they have also collected a few other European titles over the years.
Los Blancos have been crowned UEFA Cup (forerunner to the Europa League) champions on two occasions - in successive seasons in the mid-1980s.
They won the 1985 UEFA Cup final against Hungarian side Videoton with a 3-1aggregate victory and then beat German outfit Koln in the 1986 final, emerging with a 5-3 aggregate win.
In addition to the UEFA Cup and Champions League, Real Madrid have also won the UEFA Super Cup - the meeting between Champions League and Europa League winners, founded in the 1970s -four times.