Highlights: Colombia 1-1 England (3-4 pens)
2018 Fifa World Cup quarter-final: Sweden v England
Venue: Samara Arena, Samara Date: Saturday 7 July, 15:00 BST
Coverage: Live on BBC One and Online; full radio commentary on BBC Radio 5 live and text commentary and in-play clips online and in BBC Sport app
England's players will not be "bowed by the pressure of the past", said manager Gareth Southgate after they beat Colombia on penalties to set up a World Cup quarter-final against Sweden.
It was their first shootout victory in a World Cup after defeats in 1990, 1998 and 2006.
Eric Dier scored the winning spot-kick after Jordan Pickford saved Carlos Bacca's effort in Moscow.
"Today was a special night for every Englishman," Southgate told BBC Sport.
"The fans that were here were outnumbered but I'm delighted for them and everyone at home.
"We're trying to write our own history, and I've talked to the players about that. They write their own stories. We don't have to be bowed by the pressure of the past.
"This was special but I want us to go on. I don't want to go home yet."
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'We deserved it'
Southgate and England players react to shootout win
Before the game, England had won only two World Cup knockout matches since 1990 and looked to be making it three when captain Harry Kane gave them the lead from the penalty spot.
But in the third minute of stoppage time at the Spartak Stadium, Colombia defender Yerry Mina headed home to take the game into extra time and then to penalties.
Jordan Henderson's effort was saved by David Ospina, but Colombia's Mateus Uribe hit the crossbar before Pickford dived to his right to deny Bacca with his left hand.
England will play Sweden, who beat Switzerland 1-0 earlier on Tuesday, at 15:00 BST in Samara on Saturday, live across the BBC.
Quarter-final TV schedule
World Cup Daily: The England win on penalties pod
"Fantastic," said Southgate. "We deserved it as well. We played so well in the 90 minutes.
"We showed resilience to come back from huge disappointment and kept calm. It's huge credit to all our players and staff.
"Shootouts are tough. We had talked long and hard about owning the process of a shootout. They kept calm. The players have taken it all on board. It's a special moment for us.
"We looked at technique, how we needed to be as a team, the goalkeeper's role.
"But now I'm thinking about Sweden. They are another team we have a poor record against. We have underestimated them for years."
Pickford saves, Dier scores - England win penalty shootout
'Players fall in the box - it's hurtful'
In a tempestuous game, six Colombia players were shown yellow cards, including Wilmar Barrios for what looked like a headbutt in the Colombia penalty area on midfielder Henderson.
Colombia players also surrounded referee Mark Geiger for about three minutes after he awarded a penalty for Carlos Sanchez's foul on Kane.
Colombia manager Jose Pekerman said: "People in England or others should not think of Colombia players like this. It's a very competitive game.
"England have a great weapon in the air. Players fall in the box. They collide and fall. It's hurtful. You have to try and stand in the shoes of the players. They are subject to situations which shouldn't be present in football.
"These interruptions are bad. It's OK, but when there are so many fouls and interruptions that's not good. We have to find the right balance so both teams can play with the same intentions.
"We should not only look to Colombia but also England's players. In the next match England will be more careful. Today we were on the receiving end of this. It's been so obvious, too obvious."
Southgate said: "We didn't rise to it in general, which was brilliant. A couple of times we lost our cool.
Mina's dramatic equaliser takes game into extra time
"It looked like our fans were outnumbered five to one. It was an away game. To deal with it all was exceptional.
"There were many, many fouls in the game and I do not think we committed anywhere near the number they did.
"We kept our composure in a really difficult environment."
'We stepped up when it mattered'
England celebrate
England won their first World Cup shootout in four attempts
Kane leads the race for the Golden Boot as the topscorer in the tournament, having netted six goals in three games - two more than Belgium striker Romelu Lukaku.
"We played well, we controlled the game and it hits you hard when something like that happens," Kane said of Mina's equaliser.
"But it shows what we're made of. We had to go again in extra time and then the penalty shootout.
"It's been terrible for us over the years - of course we know that - and to step up when it mattered and do what we did, I'm so proud of everyone involved."
Kane and Marcus Rashford scored from the spot for England before Henderson missed, but Kieran Trippier levelled and Dier sealed victory by beating Ospina low to his right.
"We're a young squad but we learnt a lot out there today and we would have grown up a lot too," said Kane.
"We're in a great position and that could be a big moment going forward in the tournament.
"We stepped up when it mattered. We've just got to settle down and go again on the weekend."
'I was in a massive whirlwind'
England penalty record
England have won two and lost six penalty shootouts in major tournaments
Pickford made a stunning save - diving high to his left - to deny Uribe in stoppage time, but the resulting corner led to Colombia's goal.
The Everton keeper was questioned for conceding Adnan Januzaj's strike in the defeat by Belgium in the final group game.
Pickford, 24, said: "I was in a massive whirlwind but I saved it with my left hand.
"I've been criticised for going with my top hand, but as long as you save it that's all that counts.
"I might be young but I've got good mental strength and experience and I used that today.
"It's a great night to win a penalty shootout. Ideally we don't want to be going to a penalty shootout but we are delighted for the fans and the whole country."
'We handled it perfectly'
England defender Kieran Trippier: "We've practised [penalties] after loads of training sessions when we've all been fatiguing, but I had full faith in all the boys.
"With my penalty, I just stick to one spot and put it there. I'm absolutely delighted I could score for my team.
"I believe in my own ability and I believed that I could score. Hendo missed but we're all behind him and we couldn't be happier for Picks and Eric Dier.
"We had to dig deep in this game. Colombia did well - they put us on the back foot for 20 minutes - and we handled the game perfectly.
"We didn't change the way we played. We carried on playing out from the back like we do in training and like the gaffer wants us to do.
"They were trying to wind us up but we kept our cool heads. We knew they were going to taunt us before the game."
England defender Harry Maguire: "We've worked tirelessly on them (penalties). The gaffer has been reiterating it's not all about luck; it's a skill under pressure and the boys did it well. The staff have studied penalties for weeks and it's paid off tonight.
"They (Colombia) did everything they could to try and frustrate us - falling on the floor, rolling about and continuous fouling. It was a tough game to get any rhythm.
"We controlled the game for the 90 minutes then the big sucker punch was at the end in the corner. Maybe we should deal with it better.
"They threw bodies in the box and it was a bit difficult to take. We could have quite easily gone under at that point but the boys showed great courage and character to come back.
"People have been going on about 'it's coming home', and it's great to enjoy tonight. We've got another big game coming up and one we're going to look forward to."