The last two quarter-final places are up for grabs as England's Wembley showdown with Germany recalls past dramas, while Sweden take on Ukraine at Hampden.
What is happening at EURO 2020 on Tuesday?
England face Germany at 6 pm CEST at Wembley Stadium in London.
Sweden play Ukraine at 9 pm CEST at Hampden Park in Glasgow.
What are today's key EURO 2020 talking points?
England get a chance to exorcise ghosts of the past when the long-standing but uneven rivalry with Germany witnesses its latest episode at Wembley. Home fans will be hoping that a national hang-up can finally be banished along with the painful statistics trotted out each time this fixture comes around: since their only World Cup win in 1966, England have never beaten the Germans in a knock-out phase at any major tournament.
"Most (England players) were not born when a lot of those games happened, it is an irrelevance for them," said coach Gareth Southgate, who missed the penalty that shot England out of Euro '96 in the semi-final. He revealed that England had been studying German football to find the secret to their success since the 2014 World Cup in Brazil.
"Well I think that all the matches that have taken place between England and Germany, you talk about them for years afterwards. This is match that electrifies everybody," said Germany coach Joachim Low.
Trips to Scotland are rare for Sweden and Ukraine, whose thoughts will be fixed anywhere but the Wembley showdown as they focus on their later clash at Hampden. Some 10,000 fans are expected but few can travel from the two nations due to quarantine rules.
Someone who knows both Glasgow and the stadium well is Sweden defender Mikael Lustig, who won four Scottish Cup finals at Hampden during a successful eight seasons with Celtic until his departure in 2019. “It’s amazing. I haven’t been back since I left,” he said. "All my friends in Glasgow, be there!"
What happened on Monday?
Spain defeated World Cup finalists Croatia 5-3 after extra-time in a thriller in Copenhagen.
Switzerland staged the upset of the tournament so far in ousting world champions France on penalties after the two sides finished extra-time at 3-3.