Hosts France came from behind to beat the Republic of Ireland, who finished with 10 men, and reach the quarter-finals of Euro 2016. The Republic got off to a stunning start, leading in the second minute, as Robbie Brady converted a penalty after Shane Long was fouled in the box. But the French hit back through Antoine Griezmann, who nodded in the equaliser before driving in the winning goal. Shane Duffy was then sent off for a professional foul on Griezmann. Didier Deschamps’ side will face England or Iceland in the next round at Stade de France on Sunday, 3 July (kick-off 20:00 BST). However, defender Adil Rami and midfielder N’Golo Kante will miss the match through suspension, after picking up their second bookings of the tournament.

Striker Long had said before the match that his side were not motivated by “revenge” as the sides met for the first time since Thierry Henry’s controversial handball led to the Republic’s elimination in a World Cup qualifying play-off in 2009. This was the Irish’s first appearance in the knockout stages of the European Championship and their pocket of fans dressed in green at one corner of the stadium in Lyon responded with delight as Paul Pogba bundled over Southampton’s Long and Brady converted the spot kick via a post. It could have been worse for the French had Daryl Murphy’s hooked shot not been tipped away by goalkeeper Hugo Lloris. But in the end, they did not have enough firepower up front, failing to hit the target thereafter and ending the tournament with just three goals from four matches. Under increasing pressure in the second period, Martin O’Neill’s defenders held out until the 58th minute, after which they crumbled.

Germany enhanced their status as favourites for Euro 2016 as they overwhelmed Slovakia in Lille to set up a quarter-final against Italy or Spain. Centre-back Jerome Boateng gave the world champions an eighth-minute lead with a superb 25-yard volley before Mario Gomez poked in the second. Julian Draxler, who provided a superb assist for the second, made it 3-0 with a near-post volley after the break. Mesut Ozil also missed a penalty for Germany in the 14th minute. Slovakia’s best chance fell to Juraj Kucka, whose header was brilliantly tipped over by Manuel Neuer. The last-eight tie between Joachim Low’s side and one of the other fancied teams takes place in Bordeaux next Saturday. The three-time European champions have set a standard. Their performance in Lille was arguably the most dominant by a team at this championship.

After three average group displays, this was more trademark Low. The 56-year-old is a coach who does not believe in rigid roles, and against Slovakia the movement of his attack stretched the opposition defence. Germany started in a 4-2-3-1 formation with Draxler on the left, Ozil in middle and Thomas Muller on the right of the attack, just behind striker Gomez. But Draxler often interchanged with Ozil, and Muller spread himself about the Slovak half. Jan Kozak’s side spent the match chasing the Germans, and the game, after Bayern Munich’s Boateng rifled in the first with a brilliant piece of opportunism. They should have made it 2-0 but Ozil’s tame spot-kick was easily saved by Matus Kozacik, after Gomez had been fouled by Martin Skrtel. That miss did not knock the Germans off their stride, however, as the excellent Draxler teased Kucka down the left before finding Gomez, who scored his second of the tournament. And despite playing at a lower tempo after the break, Germany still managed to score a third when Draxler placed a near-post volley high past Kozacik.

Eden Hazard scored a dazzling solo goal as Belgium defeated Hungary to book a Euro 2016 last-eight tie against Wales. The Chelsea winger was outstanding in Toulouse and capped off a good Belgium display when he cut in from the left, beat two players and fired in low. Tottenham’s Toby Alderweireld headed Belgium ahead and Michu Batshuayi made it 2-0 when he tapped in. Hazard then scored his superb goal in the 80th minute before Yannick Carrasco fired in the fourth in stoppage time. Belgium and Wales will meet in Lille on Friday. They underwhelmed at the 2014 World Cup, but the most promising Belgium squad since Guy Thys’ 1980 runners-up suggested they could be set to fulfil their potential on the big stage. At times, they made hard work of it against the Magyars, but they did create 25 efforts on goal.

Manchester City’s Kevin De Bruyne had seven of those, including a brilliant first-half free-kick that was tipped over by 40-year-old Gabor Kiraly. The 24-year-old also provided two of the four assists. Both he and Hazard were the most potent weapons, with Everton striker Romelu Lukaku failing to marry willingness with goal threat. It was Spurs defender Alderweireld who gave the Belgians a 10th-minute lead when he headed in De Bruyne’s free-kick from the left. After soaking up Hungarian pressure, they finally scored a second when Batshuayi slotted in Hazard’s square ball, only two minutes after coming on. Hazard made it 3-0 with the goal of the game. Belgium broke from the Hungary area, De Bruyne played a pass to the feet of Hazard who dived in from the left, eased past two challenges before slotting into the keeper’s bottom left. By this point, Hungary had given up the fight and were handed a knockout blow when Atletico Madrid’s Carrasco, on as a substitute, slammed in from a Radja Nainggolan through ball.