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In the semi-finals they will take on Argentina, who needed their own shootout win over the Netherlands, while England continued preparations for their last-eight clash with France on Saturday.
Here, the PA news agency looks at how Friday unfolded in Qatar.
Brazil pay the penalty
Croatia stunned favourites Brazil on penalties as the 2018 runners-up reached the World Cup semi-finals again.
Marquinhos hit the post and Dominik Livakovic saved Rodrygo’s spot-kick in the shootout as Croatia won 4-2 – with star man Neymar left in despair as the unused fifth penalty taker.
The Paris St Germain star equalled Pele’s Brazil scoring record with 77 FIFA-registered goals to give his side the lead in the first half of extra-time at Education City Stadium, only for Bruno Petkovic to level with four minutes left as the game ended 1-1.
Lionel Messi avoided the same fate as Neymar – but only after a dramatic comeback from the Netherlands.
Argentina looked to be cruising through to the last four when Messi confidently converted a penalty in the 73rd minute having created the opening goal in the first half with a sublime through ball for Nahuel Molina.
But Wout Weghorst pulled one back within five minutes and then tucked away a brave and clever short free-kick deep into 10 minutes of injury time to make it 2-2.
Extra-time brought more chances for Argentina but no goals and it was goalkeeper Emiliano Martinez who proved the hero with two saves in the shootout.
Kane and able
England fully believe they can win the World Cup, according to captain Harry Kane.
Gareth Southgate’s men are looking to go all the way after losing in the semi-finals of the 2018 World Cup and the final of the European Championship last summer.
“We lost in the Euros by a couple of kicks of the ball and we have entered this tournament believing we can win and it is about trying to push on,” said Kane.
“We go into the (France) game with more belief than we did in 2018. We know that we’re a very good team and there are good teams in this tournament. If we did lose tomorrow, we would be as disappointed as anyone.”
Ronaldo a team player
Portugal boss Fernando Santos admitted Cristiano Ronaldo was unhappy about being left out of the starting line-up but denied he threatened to leave the World Cup.
The veteran forward only came on in the closing stages of the 6-1 win over Switzerland in the last 16, and Portuguese media claimed Ronaldo was ready to walk out on his team-mates.
But Santos said ahead of their clash with Morocco on Saturday: “We met and I explained why he would not be one of the starters. Cristiano, for obvious reasons, was not very happy about it. He has always been a starting player.
“He said, ‘Do you really think it’s a good idea?’ But we had a normal conversation. I explained my viewpoints, he accepted. He has never told me he wanted to leave our national team.”
Raheem Sterling was back in Qatar on Friday and training with his England team-mates – but he may not be in contention to start against France.
The 28-year-old Chelsea forward did not feature in the last-16 win over Senegal and flew home amid concerns over his family’s wellbeing following an incident at his home in Surrey.
England boss Southgate said: “He wanted to train today. Normally we wouldn’t do that, with him having been on a long flight, but it was a lighter session. He will be involved tomorrow, but what that looks like I have got to decide.”
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Tweet of the day
Quarter-finalsSaturday, December 10Morocco v Portugal (1500GMT, ITV1)England v France (1900GMT, ITV1)