The 2000's were a dry time, Hungary had no notably good players, and never even qualified for a large Soccer tournament. There only tournament was the olympics. They competed quite poorley in the olympics. Hungary was in a dry Spell, they werent playing well, had no big appearences, and were just not performing. Until 2 players, Balasz Dzsuzsak and Zoltan Gera. These two were extremely good players epcecially considering they came from Hungary Gera Played in Britain For West Brom, and actually played quite well. As for Dszuzsak he bounced around, but never really stayed at one club for too long, He was just more of a free agent type of player.
These two combined with a decent starting eleven led them to qualification for the 2016 euros. And for the first time in decades, hungary actually did quite well, they played solid, and even tied with portugal, who ended up winning, which means you could say that hungary tied to win the euros. Hungary had a solid run, and were unfortunately beaten out by Belgium, a team who was all around great. Hungary tried there hardest but eneded up loosing 4-0. Hungary were finnaly able to break there way into a national tournment, and although they didn't qualify for 2018 world cup they still were able to make it to the 2016 euros which ended an over 20 year drought of non-qualification.