We look back at six great ties at this stage since a quarter-final round was introduced with the tournament's expansion to 16 teams in 1996.
The tension inside Wembley was palpable as England, buoyed by a brilliant 4-1 victory over the Netherlands in their last group game, laboured against a promising Spain. La Roja were twice denied by an offside flag before carving open the England defence moments before half-time; Javier Manjarín was clean through but hesitated long enough for David Seaman to block.
Extra time was required, with the golden goal in play for the first time. It was not forthcoming, though, and England claimed a rare penalty shoot-out win best remembered for Stuart Pearce's celebration as he exorcised the ghost of his miss in the 1990 FIFA World Cup semi-final against West Germany.
France were the dominant team of 2000 and eventual winners of the tournament, but Spain pushed them ever so close in the Bruges quarter-final. Zinédine Zidane set Les Bleus on their way just after the half-hour, but Gaizka Mendieta's spot kick restored parity.
France were back in front before the interval after a Patrick Vieira run was capped by an even better finish from Youri Djorkaeff. Spain squandered a glorious late chance to force extra time when Raúl González sent a penalty over the bar. France went on to lift the crown in thrilling style.
A game that had everything. Michael Owen put England ahead in Lisbon with an almost balletic goal – becoming the first England player to score in four straight major tournaments – but England lost 18-year-old wonderkid Wayne Rooney to injury and Hélder Postiga equalised.
Sol Campbell had a 90th-minute effort ruled out and Rui Costa struck for Portugal in extra time, only for England's Frank Lampard to earn penalties. In a typically tense shoot-out, David Beckham missed and Ricardo saved from Darius Vassell before sensationally converting himself, as Portugal prevailed in sudden death.
This one is included more for shock value than anything. Nobody could have predicted that Greece would not just beat France for the first time ever, but would go on to win the championship.
Greece thought they had the advantage in Lisbon when Giorgos Karagounis's free-kick was met at the far post by Kostas Katsouranis but goalkeeper Fabien Barthez was adjudged to have prevented the whole ball crossing the line. However, with France toiling, Angelos Charisteas's 65-minute goal settled it ... and the rest was history.
Where to start? Turkey booked their first EURO semi-final as a fine match in Vienna was decided on penalties after the two sides had swapped goals in the closing moments of extra time. First, Ivan Klasnić nodded in Luka Modrić's cross with a minute left in the overtime period.
Yet, for the third game running, Turkey hit back even later to force the first shoot-out of the finals when Semih Şentürk drove in via a deflection. They then proceeded to triumph 3-1 on penalties, Rüştü Reçber saving Mladen Petrić's kick after earlier misses by Modrić and Ivan Rakitić.
Considering Wales were in just their second major tournament, 58 years after the first, few thought they could equal their run to the 1958 World Cup quarter-finals, let alone better it. Particularly so once fate paired them with a Belgian side stacked with stellar talent, who duly took a 13th-minute lead through Radja Nainggolan's long-range bullet.
But on the half-hour in Lille, Ashley Williams headed in Aaron Ramsey's corner, and ten minutes into the second half a player who had entered the finals without a club, Hal Robson-Kanu, brilliantly turned inside the box and shot in. Belgium pushed, but Welsh substitute Sam Vokes settled matters with five minutes left. "You dream about nights like this," said manager Chris Coleman. Wales fell to eventual champions Portugal in the semis having already achieved the seemingly impossible.