Los Blancos booked their spot in the final four courtesy of a 3-1 aggregate victory over Liverpool in the quarter-finals, while Chelsea survived a late scare against Porto to beat the Primeira Liga giants 2-1 over two legs.
The hosts go into this game on the back of a disappointing goalless stalemate with Real Betis in La Liga, whereas Chelsea boosted their top-four prospects with a 1-0 win at West Ham United.
Match preview
In a turn of events that some have described as karma, European Super League clubs have not had it all their own way on the pitch recently. Arsenal lost in laughable fashion to Everton, Liverpool conceded a last-minute equaliser to Newcastle United, and Real Madrid missed the chance to go top of La Liga as they were held to a 0-0 draw against Real Betis on Saturday night.
As Florentino Perez - now football's public enemy number one - watched on, Real's attackers were nullified by Manuel Pellegrini's defence as the reigning champions missed the chance to return to the summit, with Altetico Madrid and Barcelona now able to capitalise when they return to action later on Sunday.
Despite being hit with the threat of expulsion from the Champions League due to their involvement in the widely-condemned European Super League - a project in which president Perez acted, and continues to act as the ringleader - Real's semi-final with Chelsea will go ahead as planned as they seek a 14th continental crown.
While Los Blancos could not assert their dominance over their opponents in the group stage, Atalanta and Liverpool have both fallen victim to the superiority of Zinedine Zidane's side in the knockout rounds, although the Frenchman had a combination of his defenders and wasteful Reds finishing to thank for a goalless draw at Anfield last time out.
Nevertheless, an inspirational first-leg performance from Vinicius Junior in the quarter-finals proved pivotal as Real Madrid consigned their miserable last-16 finishes of the past two seasons to history, and the last three times that Los Blancos have appeared in the final four, they have gone on to lift the trophy.
The visit of Chelsea deserves a Bernabeu at full capacity rather than a behind-closed-doors fixture at the Alfredo Di Stefano Stadium, but Zidane's players have not allowed such inconveniences to distract them so far, so they should not allow the Super League debacle - however impactful it may be - to do so either.
While the goalless stalemate with Betis represented a third 0-0 in four games across all competitions for Real, they have strung together a 17-game unbeaten run across all competitions since losing 2-1 to Levante on January 30, and Zidane's rearguard now boasts four consecutive clean sheets.
Chelsea need no lessons in keeping attackers at bay, but during their 17-game unbeaten run, no team has managed to breach Real's defence more than once in a match, and they won five in a row on home soil before being forced to settle for a point against Betis.
Furthermore, Los Blancos have conceded just two goals in their last five Champions League matches and have won nine of their last 10 knockout ties in the tournament, but Chelsea are daring to dream under Thomas Tuchel and should not be short of confidence on the plane to Spain.
Tuchel's flabbergasted reaction to Timo Werner's second-half miss against West Ham somewhat epitomised the striker's time at Chelsea so far, but thankfully for the former RB Leipzig man, he had already ended his goal drought with a decisive first-half strike at the London Stadium.
Werner had failed to score in any of his last seven Premier League fixtures before Saturday's London derby, but he was on hand to meet Ben Chilwell's cross and calmly slot home to propel Chelsea to a 1-0 win, and crucially, a vital three points in the race for a top-four finish.
However, the game was overshadowed by yet another controversial VAR decision - a weekly occurrence in the Premier League nowadays - as Fabian Balbuena caught Chilwell after clearing the ball and was comically given a red card by referee Chris Kavanagh, and David Moyes made his feelings very clear after the full-time whistle.
West Ham's loss is Chelsea's gain, though, as the Blues established a three-point lead over their capital counterparts in the top four of the table, while Joe Willock's equaliser in the dying embers against close challengers Liverpool also saw the Stamford Bridge faithful sing an Arsenal player's praises at the weekend - a very rare sight indeed.
Tuchel also has an FA Cup final to prepare for, but winning the biggest prize of them all in his first half-season at Stamford Bridge would not just add another trophy to the glistening cabinet, it would also go a long way to ensuring his stay in one of the most unforgiving jobs in the game.
While Real Madrid have enjoyed a spate of clean sheets recently, Chelsea have also recorded three shut-outs in a row before their journey to the Spanish capital, and they have only conceded a trio of goals in the 2020-21 Champions League so far.
Two 'home' defeats have been the only blots on Tuchel's notebook so far, as the former Borussia Dortmund and Paris Saint-Germain boss has navigated his first 10 away games at Chelsea unbeaten - becoming the first manager in the club's history to do so - and the Blues have ended up on the winning side on eight of those occasions.
Having already ended their last-16 hoodoo of the past few seasons, Chelsea are appearing in the semi-finals of the Champions League for the first time since 2014 - when they were dumped out by Atletico Madrid - and the most recent time before that was their triumphant run in the 2011-12 edition.
This game would normally be classed as a blockbuster tie for the neutrals, but given the calamitous off-the-pitch events that have overshadowed the footballing world this week, those who do not support a member of the 'Dirty Dozen' may struggle to pick a preferred winner as the sides battle to meet Manchester City or PSG on May 29.
Real Madrid Champions League form:
Real Madrid form (all competitions):
Chelsea Champions League form:
Chelsea form (all competitions):
Team News
The big news from the Real Madrid camp is that Eden Hazard is fit and raring to go after coming off the bench against Betis, but with the former Chelsea man struggling so much with injuries since moving to the Bernabeu, Zidane may not risk him from the off.
However, one alteration in attack could see the hero of the hour against Liverpool - Vinicius - replace Rodrygo out wide, as he did after 59 minutes in the weekend's draw with Betis.
Toni Kroos has been struggling with muscular discomfort but should return for the first leg to form a familiar midfield with Casemiro and Luka Modric, which would see Isco drop down to the bench.
Federico Valverde remains in isolation after testing positive for coronavirus, and Zidane could make do without three defenders as Sergio Ramos (calf), Lucas Vazquez (knee) and Ferland Mendy (calf) keep each other company in the treatment room, although the latter may be available for this tie.
The hosts have been boosted by the recent returns of Dani Carvajal and Raphael Varane, though, and Nacho Fernandez will hope to keep his spot at left-back over Marcelo.
While Hazard and Thibaut Courtois look to influence the game against their former club, Mateo Kovacic will not be reuniting with his former Blancos teammates, as Tuchel has confirmed that a hamstring injury will keep the midfielder out of the first leg.
Aside from the ex-Real Madrid lynchpin, Chelsea have no other injury or suspension concerns for the first leg, as Thiago Silva managed to come through the clash at the London Stadium unscathed following careful management by Tuchel.
Silva should hope to form a familiar back three with Cesar Azpilicueta and Antonio Rudiger, and should the Spaniard be pushed further back, Andreas Christensen could drop out as Reece James returns on the right.
Jorginho and N'Golo Kante will continue to man the engine room in Kovacic's absence, but competition for places in Tuchel's front three could hardly be greater.
Mason Mount has established himself as a regular fixture in Tuchel's first XI, and Werner will not want to be dropped after ending his goal drought, but Kai Havertz could lead the line as Christian Pulisic makes way.
Real Madrid possible starting lineup:
Courtois; Carvajal, Varane, Militao, Nacho; Casemiro, Kroos, Modric; Asensio, Benzema, Vinicius
Chelsea possible starting lineup:
Mendy; Azpilicueta, Silva, Rudiger; James, Jorginho, Kante, Chilwell; Mount, Werner; Havertz
Head To Head
Real Madrid and Chelsea have only ever met three times down the years, and the Spanish side have failed to win any of those meetings - losing twice and drawing once to the Blues since 1971.
Peter Osgood was Chelsea's hero when they beat Real Madrid in the 1970-71 European Cup Winners' Cup after a final replay, and the two sides have not locked horns since the 1998 UEFA Super Cup, where Gus Poyet came off the bench to score the winner in a 1-0 Chelsea victory.
Individual statistics also favour the Blues, as Tuchel has not lost any of his four games against Real Madrid as a manager, while Edouard Mendy - who has shipped just two goals in nine European games this term - could equal Keylor Navas's record of the fewest goals conceded in his first 10 Champions League matches, which he set at Real Madrid between 2014 and 2016.
We say: Real Madrid 1-0 Chelsea
Another goalless stalemate for Real Madrid in the first leg is not beyond the realm of possibility, as two of Europe's tightest defences hope to maintain their impenetrable nature and avoid falling behind at half time in the semi-final.
Tuchel's attacking contingent have not gelled consistently - as evidenced by a wave of 1-0 victories since the German took over - but we can see the Blues ending up on the wrong end of that scoreline in the first leg, as Zidane's men look to prove their prowess with a fit-again Hazard in tow.