Across the years, the Champions League has seen many sides fight against the odds to secure stunning comeback wins.

Europe's favourite competition has long been a tournament of unimaginable reversals of fortune — but which ones are the best?

LiveScore take a walk down memory lane and pick out the most memorable two-legged affairs.

5. Ajax 5-3 (agg) Real Madrid — 2019

Ajax had already surprised many in the group stage of the 2018-19 campaign by drawing home and away against German powerhouses Bayern Munich.

Nevertheless, the Dutch side looked unlikely to come back from a 2-1 home loss to Spanish giants Real Madrid in the first leg of their last-16 contest.

But they produced one of the biggest upsets in recent history against Europe's most successful side, as Hakim Ziyech slotted in an early opener before David Neres added another.

Then came Dusan Tadic firing a blinder past Thibaut Courtois before Lasse Schone topped the night off with a free-kick into the top corner, making it 4-1 after Marco Asensio's late consolation.

4. Tottenham 3-3 (agg) Ajax — 2019

A matter of weeks after their triumph against Los Blancos, Erik ten Hag's side found themselves just 90 minutes away from the final.

The Amsterdam club brought a 1-0 lead back to the Netherlands after an impressive performance against Tottenham in North London.

And the hosts soon roared into a 3-0 advantage when Matthijs de Ligt and Ziyech found the net before half-time.

But in what was truly one of the most nail-biting second halves in Champions League history, Spurs forward Lucas Moura struck in the 55th and 59th minutes to leave the tie in the balance.

Mauricio Pochettino's men faced stiff resistance from Ajax stopper Andre Onana until Moura pounced six minutes into added time to rifle home and seal his hat-trick, an away goals victory and a spot in the final.

3. Barcelona 4-4 (agg) Roma — 2018

Few gave Roma hope of beating Barcelona in their 2017-18 quarter-final — and that number would have dwindled even further after their 4-1 thumping at the Camp Nou.

But back at the Stadio Olimpico for the second leg, Edin Dzeko's early opener gave the hosts a lifeline.

When Daniele De Rossi scored from the penalty spot after the break, a raucous home crowd in the Italian capital sprung into life.

Decibel levels finally reached a crescendo in the 82nd minute when Greek defender Kostas Manolas scored Roma's third, earning the Serie A side an iconic away goals triumph.

2. Barcelona 3-4 (agg) Liverpool — 2019

Impressive victories against Bayern Munich and Porto had handed Liverpool a semi-final encounter with Barcelona in May 2019.

But the Merseysiders were off the pace in the first leg at the Camp Nou, with a Lionel Messi double orchestrating a 3-0 victory for the Catalan hosts.

Anfield has a habit of staging remarkable European occasions and the second leg was one of the best.

Braces from Divock Origi and Georginio Wijnaldum secured a 4-0 win for Jurgen Klopp's men, flooring a disconsolate Barca.

1. Paris Saint-Germain 5-6 (agg) Barcelona — 2017

Two years earlier, Barcelona had been on the right end of a historic Champions League comeback.

The LaLiga side were down 4-0 after the first leg of their last-16 tie with Paris Saint-Germain, having been completely outplayed in the French capital.

A 2-0 half-time lead had given the Camp Nou faithful faint hope of a turnaround, but as the game moved into stoppage time, although 4-1 up on the night, two more goals were still required.

Neymar then netted a free-kick before Sergi Roberto stepped forward as the unlikely hero to end one of the most stunning matches in the competition's history.