Dubov won two medals at the European Youth Chess Championships: a bronze in 2006, in the U-10 division, and a silver in 2008, in the U-12.
2009
In 2009 he won the Young Stars of the World - Vanya Somov Memorial in Kirishi. In the same year he played for the Russian team that won the gold medal in the World Youth Under-16 Chess Olympiad. Dubov also won the individual bronze medal on board two. He won the Russian U16 rapid and blitz championships of 2009.
2011
Dubov played again in the World Youth Under-16 Chess Olympiad and won the team gold and the individual bronze on board one. Dubov won the Moscow Rapid Chess Championship of 2011.
In January, Dubov took part in the Tata Steel B tournament in Wijk aan Zee, where he scored 7½/13 points finishing fifth out of fourteen participants. At the Chess World Cup 2013 he reached the third round and was eliminated by Anton Korobov, after knocking out Sergey Fedorchuk and former FIDE World Champion Ruslan Ponomariov. In December, he played a friendly six-game match with Alexei Shirov called "Battle of Generations", which was won by the latter.
He won the Russian Higher League in July 2017 in Sochi, edging out Sanan Sjugirov on tiebreak. In the Russian Superfinal, which took place in St. Petersburg in December, Dubov shared 3rd-4th places with Vladimir Fedoseev, taking the bronze medal on tiebreak.
Dubov was selected as the Organizer's Nominee for the FIDE Grand Prix 2019, a stage in qualification for the World Chess Championship 2020. Dubov was enrolled in the Moscow event, the first of four tournaments for the 2019 Grand Prix cycle. The Moscow tournament was a 16-player event, with Dubov being the lowest ranked participant. After an upset victory over the highest ranked player, Anish Giri, Dubov was eliminated from the Moscow Grand Prix tournament in the quarter-finals by American grandmaster Hikaru Nakamura. In November, Dubov also competed in the FIDE Grand Prix event in Hamburg. Once again he was the lowest seeded player in the tournament, but after upset wins over Teimour Radjabov and Peter Svidler, he was in the semifinals facing Jan-Krzysztof Duda. The two matches in classical time format were drawn and the match proceeded to tie-breakers. Dubov won the first rapid game and needed only a draw to advance to the finals. He then lost what seemed to be a completely drawn endgame in the second match to send the match to a second set of tie breakers. After drawing with the white pieces, Dubov was finally eliminated by Duda.
2020
Dubov won the Lindores Abbey Rapid Challenge on June 3rd, beating Ding Liren in semi-finals and Hikaru Nakamura in the final after the match went to "Armageddon" time control.