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Before Switzerland stunned France, the Czech Republic had upset the formbook to dump out 10-man Netherlands 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.
Where to watch Czech Republic vs Denmark
TV channel: The match will be televised on ITV for free, with kick-off at 5pm BST.
Live stream: UK viewers will be able to watch the match online for free via the ITV Hub.
Live coverage: Standard Sport will bring you all the match action, analysis and reaction.