Six of the world's top 10 are still in the running, with Croatia (12th) and Morocco (22nd) - winners of penalty shoot-outs in the last 16 - the only remaining sides ranked lower by FIFA.
Here, we pick out some data highlights ahead of Friday and Saturday's ties.
Croatia vs Brazil, Friday 3pm GMT
Fresh legs could be decisive in the opening quarter-final clash between Croatia and Brazil, with the European side having needed extra-time and penalties to beat Japan in the previous round.
Brazil are the only team to have used every member of their 26-man squad - manager Tite even introduced third-choice goalkeeper Weverton from the bench in the last-16 win over South Korea.
In contrast, just 18 players have featured for Croatia, the fewest of any team remaining in the World Cup.
Eight members of the Croatian squad - including 37-year-old Luka Modric and 33-year-olds Dejan Lovren and Ivan Perisic - have played more than 350 minutes in the tournament already, compared with none of the Brazilians.
Netherlands vs Argentina, Friday 7pm GMT
Louis van Gaal's Netherlands and Lionel Scaloni's Argentina have adopted very different approaches in their paths to the last eight.
While Scaloni's side have largely dominated their opponents, with a shot count of 58 to 16 in their favour, Van Gaal's team have soaked up pressure by facing 51 attempts to 35 of their own.
However, in a vindication of their manager's tactics, the Dutch have outscored Argentina by eight to seven and conceded only two goals to their opponents' three.
Lionel Messi has been the standout individual on either side and he leads all remaining players for take-ons completed, with nine. The Netherlands have managed six between them, the fewest of the quarter-finalists.
Morocco vs Portugal, Saturday 3pm GMT
Morocco were the only team to defeat a higher-ranked side in the last 16 as they overcame Spain for a place in their first World Cup quarter-final.
As the tournament's lowest remaining scorers (four), Morocco will again start as underdogs against the joint-highest scorers, Portugal (12).
There could be plenty of long shots in this game, with roughly half of both sides' goal attempts coming from outside the penalty area.
Morocco rely on wide areas for attacking threat with 75 per cent of their final third entries coming down the flanks (the highest percentage of teams left). Portugal, in contrast, have recorded the lowest proportion of final third entries on the wings (60 per cent).
Cristiano Ronaldo scored the only goal when these sides met in the 2018 World Cup group stage, but he looks set to start a second successive game on the bench after his replacement Goncalo Ramos netted a hat-trick against Switzerland on Tuesday.
England vs France, Saturday 7pm GMT
The last of the quarter-finals pits the tournament's in-form team against its star player.
England have scored 12 goals and conceded just two in an unbeaten run to the quarter-finals, while France's Kylian Mbappe has netted five times and provided two assists in a series of spellbinding displays.
Mbappe is also the World Cup's leading player for shots (20), ball progressions (20) and receiving the ball between the opponent's midfield and defensive lines (110).
However, Gareth Southgate is arguably able to call on a wider array of attacking talent than his counterpart Didier Deschamps.
Eight different players have scored for England compared with just three for France, while Southgate's side lead the quarter-finalists for shot accuracy (46 per cent on target). France, on the other hand, have been the most wayward (34 per cent).