Video lesson - GM David Navara

In 2001, aged 16, he made his debut on the Czech national team in the European Team Chess Championships, where he scored 7/9 points. He received the title Grandmaster one year later, three days before his 17th birthday.

In 2003, he won the open section of the Rubinstein Memorial. Adult career Ranked 14th, he finished sixth in the 2004 European Individual Chess Championship in Antalya scoring 7½ points (+5−2=5), including a draw against the eventual champion Vassily Ivanchuk.

This result qualified Navara for the 2005 FIDE World Cup, where he was eliminated by Predrag Nikolić in the first round.

In 2006, at the 37th Chess Olympiad he scored 8½ points from 12 games against world-class competition. The next year, Navara was invited for the first time into the supertournament in Wijk aan Zee, where he replaced Alexander Morozevich. Navara, nicknamed Navara Express by organizers, gained 6½ points in 13 games (+3−3=7), including wins against Ruslan Ponomariov and Magnus Carlsen (and draws with black pieces against Vladimir Kramnik, Viswanathan Anand and Veselin Topalov), and finished in 7th place.

In August 2007 Navara finished first in the Ordix Open, a rapid tournament part of the Chess Classic Mainz festival, with a score of 9½/11 on progressive score tiebreak. The following month, he played in the Czech Coal Carlsbad tournament in Karlovy Vary, where he finished third, scoring half a point behind the winners, Ruslan Ponomariov and Sergei Movsesian.

Two months later, Navara participated in the FIDE World Cup. He beat Alexander Ivanov of US in the first round and was defeated by Sergei Rublevsky in the second round after tie-breaks. In 2007–2008 Navara played in the "Torneo di Capodanno" in Reggio Emilia, Italy, scoring 3/8 (+1−3=4).

He played in the FIDE Grand Prix tournament in Baku in 2008, scoring 5½/13 (+2−4=7). At the 2011 Tata Steel Tournament in Wijk aan Zee, Navara competed in the "B" group against other strong GMs like Wesley So, Lê Quang Liêm, Luke McShane, Vladislav Tkachiev, Zahar Efimenko, and others. Navara tied for first place with Luke McShane by finishing with 8½/13. While McShane finished ahead on tie-breaks, both players received invitations to the top "A" group next year.

Later in the same year, Navara also took part in the FIDE World Cup; he lost to Alexander Grischuk in the quarterfinals of the competition. The following year Navara won the individual gold medal on board two at the 40th Chess Olympiad in Istanbul playing for the Czech team. He won the European Blitz Chess Championship in 2014.

In April 2018, he participated in the fifth edition of Shamkir Chess, finishing tenth with a score of 2½/9 (+0−4=5).