We look at the match-ups, all of which are taking place in the United States.
France v Morocco
Imperious France have lived up to their billing as World Cup favourites, sweeping through the group stage and swatting aside Sweden before edging past Paraguay in the last 16.
It is difficult to see any team keeping Didier Deschamps’ men quiet, given their embarrassment of riches in attack, including Kylian Mbappe, Ousmane Dembele, Bradley Barcola and the wonderfully creative Michael Olise.
But unbeaten Morocco will not be fazed by facing the two-time world champions after seeing off the Netherlands on penalties and crushing co-hosts Canada 3-0 in the last 16.
The North African team will have revenge on their minds in Boston after they lost to France in the semi-finals four years ago in Qatar.
The Atlas Lions created history by becoming the first African team to progress to the last four in 2022 and will be keen to match that feat.
Spain v Belgium
In beating Portugal 1-0 on Monday, Spain became the first team in tournament history to record six consecutive World Cup clean sheets.
Luis de la Fuente’s European champions do not always set pulses racing but they are strikingly efficient and comfortable on the ball.
Barcelona star Lamine Yamal has netted just once in five games but Mikel Oyarzabal has scored four times, including twice in a 3-0 win against Austria in the last 32.
Belgium go into the match in Los Angeles on the back of a 4-1 thumping of co-hosts the United States.
That came after they rallied from two goals down in the last 32 to beat Senegal 3-2 in extra-time.
The World Cup is likely the last hurrah for the remainder of the nation’s so-called Golden Generation, including Kevin De Bruyne and Romelu Lukaku, who will be desperate to leave the stage on a high.
Norway v England
England’s defenders are used to facing Norway hotshot Erling Haaland in the Premier League — but whether they can handle him is another story.
Thomas Tuchel’s men arrived in the United States among the favourites to win the tournament for just the second time in their history.
Captain Harry Kane and Jude Bellingham have been the standout players so far, scoring 10 of the team’s 11 goals, including all three in a gripping 3-2 win against Mexico.
England, reduced to 10 men, had to dig deep to see off the co-hosts in a result that will infuse them with confidence ahead of their meeting with Norway.
But they will come up against a team in Miami led by the irrepressible Haaland, who has scored seven goals so far as he chases the Golden Boot.
The Manchester City man has netted in each of his past 14 competitive outings for Norway — 27 goals in total — and is bound to create problems for England’s shaky defence.
Argentina v Switzerland
Lionel Messi’s Argentina have come through two almighty scares to set up a quarter-final against Switzerland.
The defending champions were taken to extra-time by World Cup debutants Cape Verde before prevailing 3-2.
Then in the last 16 they looked down and out when trailing 2-0 against Egypt before an astonishing comeback, with Messi at the centre of the action.
Head coach Lionel Scaloni will know his team cannot keep testing fate as they chase a fourth World Cup crown, but they have shown they can never be counted out.
Now they face Switzerland in Kansas City, who beat Colombia on penalties in Vancouver after a goalless draw.
The Swiss, who are into the last eight for the first time since they hosted the tournament in 1954, are an organised outfit and will likely be tough to break down.
