UEFA.com picks out the players who have shone in the second legs, including Joe Hart, Christian Fuchs and Klaas-Jan Huntelaar, whose heroics were all in vain.
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GK Joe Hart (Manchester City)
"Joe Hart is a phenomenon," concluded Lionel Messi. For 90 minutes the England goalkeeper was the last line in a City defence which threatened to be overrun by Messi, Neymar and Luis Suárez – he made ten saves in a 1-0 loss, none of them easy. Not many encounter Messi in full flow and live to tell the tale. Fewer still come out of it claiming to "really enjoy it".
DF: Christian Fuchs (Schalke)
The right-back provided a valuable attacking outlet as Schalke came close to achieving what had looked impossible at the Santiago Bernabéu. Fuchs put Schalke 1-0 up in the 20th minute, driving beyond Iker Casillas after finding himself unmarked in the penalty area, and his corner teed up Leroy Sané to make it 3-3 – yet Schalke just fell short.
DF: Thiago Silva (Paris)
The Paris captain was magnificent as the Ligue 1 title holders prevailed at Chelsea on away goals. Not only did he defend staunchly as Chelsea strove to secure the tie, he popped up with a superb headed goal to take Paris through just when it seemed their hopes were over in extra time.
DF: David Luiz (Paris)
Silva's centre-back partner Luiz was equally impressive back at his former Stamford Bridge home. And he admitted he forgot himself when he nodded in a brilliant 86th-minute equaliser, saying: "It was difficult for me because I was so happy to win, but I was also so happy at Chelsea."
DF: Aymen Abdennour (Monaco)
The Tunisia centre-back typified Monaco's indomitable spirit, putting his body on the line as they resisted an Arsenal onslaught to advance on away goals. As he celebrated at Stade Louis II he wore a Gunners shirt, souvenir of a memorable night; though so tight was his marking at times, it seemed he had been sporting it most of the evening.
MF: Yacine Brahimi (Porto)
Porto stormed to a 4-0 success over Basel to book a quarter-final return after six years away – and they were set on their way by a typically excellent Brahimi free-kick. The Portuguese side never looked back after that and Brahimi was a fizzing presence, even if his goal was later eclipsed ...
MF: Mario Suárez (Atlético)
Atlético went into their home leg 1-0 down to Leverkusen but in the tighest of return matches, Suárez ensured the 2014 runners-up stayed in the hunt as his deflected effort wiped out the deficit. Excellent in midfield, he also coolly converted his penalty in a shoot-out in which five were missed or saved.
MF: Casemiro (Porto)
Porto netted four wonderful goals against Basel but Casemiro, the Brazilian on loan from Real Madrid, topped the lot. Lining up a set piece 30 metres out, he had only one thing on his mind as he speared it into the top corner – a strike as true and forceful as his presence in Porto's midfield.
FW: Carlos Tévez (Juventus)
Before this term the Argentinian had six goals in 33 UEFA Champions League games; his double in Dortmund matched that total in eight outings in the current campaign. He put Juve on course for a second quarter-final in three years with a powerful drive from range on three minutes and, after unselfishly inviting Álvaro Morata to make it 2-0, supplied the third himself with another cool finish.
FW: Lionel Messi (Barcelona)
"They've got a lot of belief and they've got Lionel Messi," said Hart as he returned the compliments and explained why City had fallen short. The Argentina No10 has begun 2015 with a bang, and while he did not score at the Camp Nou he did just about everything else right. Including, of course, carving out the solitary goal for Ivan Rakitić.
FW: Klaas-Jan Huntelaar (Schalke)
Another of Schalke's Bernabéu heroes, the ex-Madrid ace spearheaded the visiting challenge with two contrasting goals. Moments after a thunderous strike had come back off the woodwork, the Dutchman reacted quickest when Iker Casillas only parried Max Meter's shot; then, with time running out, he smashed in off the underside of the crossbar to herald a grandstand finish.