Liverpool crashed out of the UEFA Champions League after losing 3-2 after extra time against Atletico Madrid on Wednesday at Anfield.
The result allowed the La Liga giants to advance 4-2 on aggregate, with the holders running out of steam in the last 16.
Paris Saint-Germain eliminated Borussia Dortmund 3-2 on aggregate after winning 2-0 in the French capital.
Atletico and PSG join RB Leipzig and Atalanta in the next round after they knocked out Tottenham Hotspur and Valencia, respectively, on Tuesday.
Liverpool 2-3 Atletico (Atleti win 4-2 on aggregate)
PSG 2-0 BVB (PSG win 3-2 on aggregate)
Liverpool couldn't find a way into the quarter-finals against a dogged Atleti team intent on frustrating the Premier League leaders.
Diego Costa almost shocked Anfield with an opener in the first minute, but the striker's effort went the wrong side of the post.
Liverpool put their foot down on the accelerator in response, and Diego Simeone's men appeared happy to slow the game down to a walking pace when possible.
Mohamed Salah and Sadio Mane both were busy in the final third, but the opener came from an unlikely source when Georginio Wijnaldum headed home two minutes before the interval.
Alex Oxlade-Chamberlain provided the perfect cross for the Netherlands international, and the midfielder's powerful header beat Jan Oblak.
Andrew Robertson's second-half header rattled the Atletico crossbar with the goal at his mercy, and the Scot went close once again with 10 minutes remaining, but Liverpool's constant pressure failed to pay dividends.
The game went into extra time with the aggregate score at 1-1, and it seemed Liverpool would advance when Roberto Firmino quickly found the back of the net.
However, a mistake from Reds goalkeeper Adrian opened the door for Marcos Llorente, and the Atleti substitute found the bottom corner to level the tie once again.
A counter-attack from the visitors helped Llorente to his brace, and Alvaro Morata scored in the final seconds to secure a historic night for Simeone's battling side.
PSG controlled the second leg against BVB at the Parc des Princes and impressively overturned the 2-1 first-leg deficit.
The match was played before a near-empty stadium because of measures to prevent further spread of the coronavirus.
Kylian Mbappe only started on the bench after suffering with a throat infection, but Neymar was enough to inspire PSG to victory.
The Brazilian headed home after 28 minutes when BVB failed to defend Angel Di Maria's corner, and it was 2-0 after Juan Bernat flicked the ball past Roman Burki just before half-time.
Dortmund showed good intentions in the second half without fully concerning the hosts. PSG were happy to keep the ball with a slim aggregate advantage in their pockets.
The visitors failed in their efforts to force the tie into extra time, and BVB's Emre Can was shown a red card after pushing Neymar to the floor in the closing moments.