But incredible comebacks have happened before in football and Roma have even played their part in one of the most incredible of them all.
Manchester United beware – commanding leads have fallen in Europe before and here, Sportsmail looks back at some of the most epic comebacks on the continent.
Ole Gunnar Solskjaer and his Manchester United team still have work to do against Roma
ROMA 3-0 BARCELONA, 2018
After being defeated 4-1 by Barcelona in the first leg of their Champions League quarter-final in 2018, the writing seemed to be written on the wall for Roma.
But they didn’t read what it said. Come the second leg at the Stadio Olimpico, Roma stunned Lionel Messi and his team with a blistering 3-0 comeback.
Edin Dzeko fired Roma ahead after only six minutes but Barca kept it to 1-0 by half-time. Daniele de Rossi made it two from the spot on 52 minutes and then, with eight minutes to go, Greece defender Kostas Manolas dealt the knockout blow to Spain’s runaway leaders in the league that season.
That result can serve as inspiration for Roma as they look to overhaul the 6-2 defeat from the first leg at Old Trafford against United on Thursday. And their comeback was certainly something Liverpool had in mind a year later.
Roma completed an astonishing comeback against Barcelona three years ago in 2018
LIVERPOOL 4-0 BARCELONA, 2019
Jurgen Klopp’s men had been humbled in an emphatic 3-0 semi-final defeat in the first leg of their Champions League tie. And while Liverpool will always rely on the aura of Anfield to achieve the seemingly impossible, their task was punctured by injuries ahead of the game to key attackers Mohamed Salah and Roberto Firmino.
Divock Origi led the line instead and put Liverpool ahead early on with just seven minutes on the clock.
But like Roma the year before, Barcelona kept the score to just 1-0 at half-time. Klopp introduced Georginio Wijnaldum for an injured Andrew Robertson at the interval and the Holland midfielder scored twice in just two minutes to put Liverpool within touching distance of a sensational comeback.
And then, 11 minutes from time, Trent Alexander-Arnold’s corner caught the Barca defence napping and Origi swivelled and turned the ball into the top corner as Anfield erupted.
Georginio Wijnaldum scored twice to inspire Liverpool to a 4-0 win against Barcelona
DEPORTIVO 3-0 AC MILAN, 2004
A throwback here to that enterprising Deportivo La Coruna side that proved to be a nemesis of so many big European side after the turn of the century.
The likes of Juan Carlos Valeron, Albert Luque and Walter Pandiani had it all to do after the defending champions Milan crushed the Spanish side in the first leg with a dominant display and a 4-1 victory.
Incredibly, Carlo Ancelotti’s men crumbled so dramatically that their three-goal advantage was erased in an extraordinary first half, with Valeron, Luque and Pandiani all scoring.
But it was substitute Fran who hit the decisive goal that knocked Milan out in the 75th minute. It took Deportivo into the semi-final where they met a Porto side who were then managed by an up-and-coming coach called Jose Mourinho.
In 2004, Spanish side Deportivo La Coruna stunned Champions League holders AC Milan
BARCELONA 6-1 PSG, 2017
A frankly extraordinary game with more twists and turns than such a one-sided scoreline suggests due to PSG’s 4-0 first-leg triumph.
Luis Suarez opened the scoring in the return game at the Nou Camp after just three minutes and it was 2-0 at half-time after a Layvin Kurzawa own goal.
A Messi penalty in the 50th got a third but just as it felt like a comeback was gaining momentum, Edinson Cavani replied for PSG and that away goal left Barcelona needed another three goals in 25 minutes.
It felt like the tie was over and as the clock reached the 88th minute without Barcelona scoring again – they were 5-3 down on aggregate and PSG must have thought it was job done.
Enter Neymar, who scored two in two minutes and then, with five minutes added on, he turned provider for Sergi Roberto to prod home his first goal of that season and spark wild scenes.
Barcelona’s comeback against Paris Saint-Germain had three goals in the last five minutes
TOTTENHAM 3-2 AJAX, 2019
Like Barcelona against PSG, the most striking thing about this comeback is how Tottenham were never at any point winning the overall tie until Lucas Moura completed his hat-trick in stoppage time of the second leg.
The Dutch side beat Spurs 1-0 in London and picked up where they left off in the second leg, taking a 2-0 lead through Matthijs de Ligt and Hakim Ziyech and 3-0 aggregate advantage.
But Lucas Moura stepped forward in the second half with an extraordinary one-man display, notching two goals in the 55th and 59th minute to galvanise Mauricio Pochettino’s men.
It looked like they were going to fall short though, until Moura went on a mazy run in stoppage time and sent a calm, low shot narrowly past the reach of goalkeeper Andre Onana.
Tottenham celebrate wildly after the Ajax fightback to make the 2019 Champions League final
CHELSEA 4-1 NAPOLI, 2012
All three of Chelsea’s Champions League final appearances have come after changing a manager in mid-season.
In 2012, it was Roberto Di Matteo who steered Chelsea to their maiden Champions League triumph but after a 3-1 defeat by Napoli in the first leg, it seemed like their season was in ruins.
That loss in Naples saw Andre Villas-Boas axed and Di Matteo put in charge for the remainder of the 2011-12 campaign.
Back at Stamford Bridge for the second leg in the last 16, goals from Didier Drogba, John Terry and Frank Lampard – around a second half goal from Gokhan Inler – took the tie to extra time.
Branislav Ivanovic got the goal that ignited Chelsea’s charge to glory, smashing the ball home from Drogab’s cut back across the six-yard box in the 105th minute.
Chelsea’s Napoli comeback set foundations for them winning the Champions League in 2012