Here, the PA news agency takes a look at how the four ties shape up.
Switzerland v Spain
(July 2, St Petersburg, 1700 BST)
The Swiss – who qualified for the last 16 as one of the best-ranked third-placed teams – delivered the biggest shock of Euro 2020 so far when they knocked out World Cup winners France following a penalty shoot-out in Bucharest, having rallied from 3-1 down with 10 minutes left.
Luis Enrique's Spain, runners-up in Group E, recovered from going behind to a calamitous own goal by goalkeeper Unai Simon to eventually beat Croatia 5-3 after extra-time in Copenhagen, where late goals from Mislav Orsic and Mario Pasalic had levelled things up in another highly dramatic encounter.
(July 2, Munich, 2000 BST)
The world's best team have lived up to their billing as Roberto Martinez's Belgium coasted through Group B with a perfect record before then dispatching holders Portugal in Seville with a fine strike from Thorgan Hazard followed by determined defending during the closing stages. Victory came at a cost, though, with the fitness of Kevin De Bruyne and Eden Hazard to be closely monitored ahead of their trip to Munich.
Italy also impressed as they won Group A ahead of Wales without breaking sweat. However, Roberto Mancini's men were stretched by a determined Austria in their last-16 tie at Wembley – and could have been behind in the closing stages but for the intervention of VAR to rule out Marko Arnautovic's header. Eventually, though, Italy ground out another result with goals in extra-time from Federico Chiesa and Matteo Pessina, before a rare breach of their defence. The Azzurri are unbeaten through 31 games, a new national record – one which will be put to the test against Belgium.
(July 3, Baku, 1700 BST)
Before Switzerland stunned France, the Czech Republic had upset the formbook to dump out 10-man Holland 2-0 in Budapest. The Dutch – who topped Group C on the back of three wins at the Johan Cruyff Arena – crumbled after defender Matthijs De Ligt was sent off for denying a goalscoring opportunity with a handball after 55 minutes. Czech forward Patrik Schick took his tournament goal tally to four and has the Golden Boot now firmly in his sights.
Denmark qualified for the knockout stage on a wave of emotion following their response after Christian Eriksen suffered a cardiac arrest in their opening group match and had to be resuscitated with a defibrillator. Kasper Hjulmand's squad, though, showed their place in the last eight is very much on merit after an impressive display ended Wales' hopes in Amsterdam.
Ukraine v England
(July 3, Rome, 2000 BST)
After losing to both Holland and Austria in Group C, Andriy Shevchenko's Ukraine were left sweating on results elsewhere to qualify as one of the third-placed teams, eventually edging out Finland on goal difference for the final slot. They then got past Sweden in a dramatic finale at Hampden Park, with a 2-1 win being secured by Artem Dovbyk's goal in stoppage time at the end of extra-time.
England reached the last 16 without conceding a goal, topping Group D after Raheem Sterling goals had sealed 1-0 wins over Croatia and the Czech Republic either side of a 0-0 draw against Scotland. Back at Wembley once again, as for the three pool games, Gareth Southgate's young squad then showed no weight of history against Germany as they won 2-0 thanks to goals from Sterling and skipper Harry Kane.