Reigning champions Real Madrid have booked their spot in the semi-finals of the Champions League courtesy of a 4-0 aggregate victory over Chelsea.
Los Blancos entered Tuesday's quarter-final second leg with a strong advantage, having recorded a 2-0 win when the two teams locked horns at Bernabeu in the reverse fixture last week.
Chelsea were much improved at Stamford Bridge but were unable to find that extra piece of quality at the vital moment, with Rodrygo's double winning it for Carlo Ancelotti's side on the night.
Real Madrid - bidding to win a 15th European Cup - will take on either Manchester City or Bayern Munich in the semi-finals of the competition, with the English champions in a strong position in their quarter-final following a 3-0 victory in Manchester last week.
Chelsea are now highly unlikely to be present in next season's Champions League, as they sit down in 11th position in the Premier League table, 17 points behind fourth-placed Newcastle United.
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Chelsea had a golden chance to take the lead in the 11th minute of the contest when Reece James's low cross fell for N'Golo Kante in a dangerous position, but the Frenchman fired his effort wide of the post.
The Blues were very much the team on the front foot in the early exchanges, with James causing a number of problems down the right, while Kai Havertz's physical presence was making it uncomfortable for Real Madrid, who did not offer too much in the opening 15 minutes of proceedings.
Los Blancos hit the woodwork in the 19th minute, though, with Rodrygo's strike from a narrow angle striking the outside of the post in a serious warning to Chelsea.
Vinicius Junior then forced Chelsea goalkeeper Kepa Arrizabalaga to make a smart save in the 28th minute, with the Brazil international working his way into a shooting position inside the penalty box.
Conor Gallagher headed over the Real Madrid crossbar from close range, but the offside flag was raised, much to the relief of the midfielder, who had passed up a brilliant chance.
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Kepa made another stop to keep out a Luka Modric effort in the 32nd minute, before Vinicius failed to convert a brilliant low cross from Modric in the latter stages of the first period, with the Brazilian slicing wide under pressure.
Karim Benzema then fired a Federico Valverde cross wide at the far post, with the opportunities starting to come on a regular basis for the reigning European champions.
Chelsea had an incredible chance to register on the stroke of the interval when a low cross from James found Marc Cucurella at the far post, but the Spaniard was denied by a brilliant save by Real Madrid goalkeeper Thibaut Courtois.
The Blues has another huge opportunity in the 51st minute, with the ball breaking for Kante inside the box following a header from Gallagher, but Eder Militao was on hand to make a brilliant block.
Militao was fortunate to escape a second yellow card for a pullback on Trevoh Chalobah shortly after, with Chelsea players incensed that the defender was not sent off.
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The home side had two chances in the period that followed, with Enzo Fernandez striking just wide of the post before Courtois kept out Havertz, who showed impressive feet in a tight area.
However, Real Madrid silenced Stamford Bridge in the 58th minute, with Rodrygo scoring to make it 1-0 to the visitors on the night and 3-0 on aggregate.
Rodrygo's pace took him past Chalobah down the left; the Brazilian's initial cross was missed by Benzema, but Vinicius was on the scene, showing brilliant composure to settle on the ball before picking out Rodrygo, who found the back of the net from close range.
Courtois denied Gallagher and Fernandez in the period that followed, before Kepa did well to deny Benzema down the other end, with both sides having opportunities to add to the scoring in the English capital.
Joao Felix, Raheem Sterling, Mykhaylo Mudryk and Mason Mount were all introduced as Chelsea looked for a route back into the tie, but Rodrygo netted another for Real Madrid in the 80th minute, with the forward converting into an empty net after being found by Valverde.
Chelsea have now lost each of their last four matches, and they will be bidding to bounce back in their next Premier League match at home to Brentford on April 26, while Real Madrid will be watching closely to see what develops in Wednesday's quarter-final second leg between Bayern and Man City.
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