Brazil seek to become the first team through to the World Cup semi-finals on Friday, while Argentina could set up a blockbuster all-South American clash if they get past the Netherlands.
After three weeks of pulsating action in Qatar, just eight teams are left standing as the 32-nation tournament heads into the final rounds of the knockout competition after a two-day break.
Five-time champions Brazil kick off the quarter-finals against surprise 2018 runners-up Croatia, with Neymar fit and firing after an ankle injury he suffered in the opening game.
"I'll be doing everything that I can to win with the Brazilian national team. That's our mission and our dream," said Neymar.
"We're getting ever closer, we've got another step to go now."
Croatia are a much-changed team from the one that reached the final four years ago, but 37-year-old Luka Modric remains the player who makes them tick.
"I agree that we did a great thing by getting to the quarter-finals but regardless of that we would like to do more," said Modric, who will come up against his Real Madrid teammates Vinicius Junior, Rodrygo and Eder Militao in the match at Education City Stadium.
"We know that the greatest match is ahead of us. Brazil are always favourites. We have to be ourselves."
Seven-time Ballon d'Or winner Lionel Messi is hoping to end his wait for a World Cup after Argentina lost to Germany in the final eight years ago.
The Copa America holders go up against the Netherlands in Friday's second quarter-final at Lusail Stadium, the venue for the December 18 final.
The two countries have met five times at the World Cup, including in the 1978 final, which Argentina won 3-1 after extra-time.
"In 2014 I was there and things ended slightly differently (from how we wanted) but I'd like to change that now," said Dutch forward Memphis Depay.
After Argentina's shock loss to Saudi Arabia in their first match, Messi has dazzled in Qatar and the Dutch will have to nullify his threat.
"We're not going to reveal our tactics to you (about stopping Messi). It would be pretty stupid to reveal your own tactics," said veteran coach Louis van Gaal.
"Messi is the most dangerous creative player, he is able to create a lot and to score goals himself. But when they lose the ball he doesn't participate much, this gives us chances," he said.
Attention switches on Saturday to the heavyweight clash between defending champions France and England.
France captain Hugo Lloris said the rivalry between the two countries was special.
"These are two great football nations and the rivalry between us also exists in other sports like rugby," he said on Friday.
"When you get to such a high level these are great battles. At an event like the World Cup there is a special flavour to a France-England game. But we are preparing for a World Cup quarter-final, regardless of the opponent."
England boss Gareth Southgate has vowed to go on the attack, despite the threat from the fleet-footed Kylian Mbappe, who is arguably the best player in the world.
"There is no point going into a game like this and just covering up and sitting on the ropes," he told ITV. "We believe we can cause problems with the ball and we intend to do that."
In the other game on Saturday, Morocco, in the World Cup quarter-finals for the first time, take on Portugal.
Portugal on Thursday denied reports that Cristiano Ronaldo threatened to quit the camp after he was benched for their 6-1 rout of Switzerland in the last 16.
Ronaldo took to social media to say that Portugal were "too united to be broken by outside forces".
By Martyn WOOD