Germany's hopes of a seventh successive European women's title were shattered on Sunday when second-half headers by Nadia Nadim and Theresa Nielsen gave Denmark a shock 2-1 victory in the quarter-finals in Rotterdam.
In Thursday's semi-finals, Denmark will face newcomers Austria who beat Spain 5-3 on penalties following a goalless draw in Tilburg.
Hosts the Netherlands, who beat Sweden 2-0 on Saturday, will face England who edged France 1-0 in Deventer in Sunday's last game thanks to Jodie Taylor's fifth goal at the tournament.
It was England's first win over France in 43 years.
Germany, who have won the Euro six times in a row and eight times overall, dominated the eventful game postponed from Saturday because of heavy rain, but Denmark's counter-attacking was eventually too much for them.
Germany were out of the blocks fast with Isabel Kerschowski drawing first blood on three minutes with massive help from Danish keeper Stina Petersen who palmed her shot from just outside the box into the goal.
But Nadim put Denmark level three minutes after the break with a bullet header from a cross by Stine Larsen and Nielsen then headed home a cross from substitute Frederikke Thoegersen with seven minutes left.
"I'm so happy that we beat Germany. It's amazing," said Nielsen. "Everybody dreams about scoring, but doing it is another thing. Why not today? It's a good day."
Denmark coach Nils Nielsen said the win was deserved as winger Katrine Veje hit the woodwork after a Nadim pass flicked on by Harder with half an hour to go, while Petersen regained her self-confidence with several brilliant saves.
"It was fairly equal in terms of the chances. Germany didn't put us under big pressure."
German coach Steffi Jones bemoaned a lack of will to win on the German side.
"There's a lot of disappointment. We weren't aggressive enough," she said.
In Tilburg, Austrian 'keeper Manuela Zinsberger became the hero after saving Silvia Meseguer's penalty with a superb dive in the shoot-out.
"It was a very intense game," said Austria coach Dominik Thalhammer.
"Spain had a lot of possession and it wasn't easy, but we defended well."
Spanish coach Jorge Vilda revamped his strikers, but his team once again resorted to a possession game with long-range shots and few clear-cut chances.
The biggest danger for Austria came from a deflected shot which bounced before Zinsberger who then cleared it off her top corner.
Substitute Jennifer Hermoso fired just over the Austrian bar before the final whistle.
At the other end, Nicole Billa missed from close range in the first half while substitute Nadine Prohaska headed straight at Spanish 'keeper Sandra Panos from a corner after the break.
"Today I think the side was good in general, but we needed maybe to move the ball quicker," said Vilda.
"Right now it's the most difficult defeat I've had."
England scored their first victory against France since 1974 owing to Taylor's shot from the right flank which French keeper Sarah Bouhaddi deflected with her palm but could not tame.
France, who lost skipper Wendie Renard to two yellow cards, had a few good chances, but Eugenie Le Sommer headed wide and Marie-Laure Delie was denied by goalkeeper Karen Bardsley.
Substitute Claire Lavogez missed from a free-kick before missing narrowly with a low left-footer, leaving France waiting for their first Euro semi-finals ever.
"I'm incredibly proud of the players. However long that game went on we weren't going to be broken down," said England coach Mark Sampson.
"This is a French team who without a doubt are one of the best in the world, but we ground out another result."
French midfielder Amandine Henry said her team had nothing to be ashamed of.
"There were two good teams and, unfortunately, tonight we have to bow out," she said.
"It was a game decided by the tiniest margins, but that's what it's like at the top level," added French coach Olivier Echouafni.