What you need to know:
In the second semi-final on Wednesday, reigning champions France take on giant-killing Morocco, the first African team ever to reach the last four of a World Cup
Lionel Messi and Luka Modric face off in a mouthwatering World Cup semi-final between Argentina and Croatia on Tuesday, desperate to seize their final chance to win football's ultimate prize.
In the second semi-final on Wednesday, reigning champions France take on giant-killing Morocco, the first African team ever to reach the last four of a World Cup.
But first all eyes will be locked on the cavernous Lusail Stadium, where Messi, now 35, will attempt to fire Argentina into the final for the second time in eight years against the 2018 runners-up.
Messi, who suffered defeat to Germany in the 2014 final, is desperate to crown his extraordinary career by emulating another Argentine great, the late Diego Maradona, who lifted the trophy in 1986.
The Paris Saint-Germain forward was a pivotal figure in Friday's stormy quarter-final win over the Netherlands, when a record 18 yellow cards were shown and players from both sides were involved in a melee as the referee fought to regain control.
Argentina coach Lionel Scaloni defended his players' conduct on Monday, insisting they had nothing to apologise for.
"The game the other day was played in the right way by both teams. That is football," said the 44-year-old Argentina coach.
"I don't buy this idea that we don't know how to win. The game was played in the right way."
Croatia, who beat Japan and pre-tournament favourites Brazil in penalty shoot-outs to reach the last four, have not won a knockout game in normal time at a major tournament since the 1998 World Cup, where they came third.
The country of fewer than four million people shocked the football world by reaching the final four years ago in Russia, where France crushed their dreams with a 4-2 win.
Croatia defy odds
Croatia, with Real Madrid playmaker Modric still the leader on the pitch at the age of 37, have again defied the odds to stand on the brink of a second successive final.
Coach Zlatko Dalic said reaching the semis for a second straight World Cup was an "extraordinary success" but he was hungry to go further.
"I'm optimistic and have full confidence in my players," he said. "They've shown their great quality and strength of character, and deserve to be in the final."
France are strong favourites to beat Morocco and take a step closer to defending their title.
But the African team's history-making run has caught the imagination of a continent and they have been backed by legions of fans in Qatar.
The match will have added spice France was Morocco's colonial power and hundreds of thousands of people with Moroccan roots live and work in the country.
France captain Hugo Lloris said the champions were guarding against complacency and were braced for a pro-Morocco crowd.
"We can only have respect and admiration for what they have done, but nothing happens by chance at this level," he said.
"They will be formidable opponents, and on top of that there will be a hostile atmosphere in the stadium," he added.
France coach Didier Deschamps said: "There is a popular fervour behind them. It will be very noisy and my players have been warned about that. They know what to expect."
Morocco's coach, Walid Regragui, said his side, also the first Arab side to reach a World Cup semi-final, were desperate to progress.
"If you get to the semi-finals and you are not hungry then there is a problem," he said.
"The best team in the tournament, Brazil, is already out. We are an ambitious team and we are hungry but I don't know if that will be enough."
Away from Qatar, the German Football Association announced a think tank of former internationals including Karl-Heinz Rummenigge and Matthias Sammer to help restore the nation's fortunes after another dismal World Cup.