Navara is a recipient of multiple Czech Chess Championships and has participated in many significant international tournaments, including the Chess World Cup, in which he reached the quarterfinals in 2011. He has faced and defeated several top players, such as Magnus Carlsen and Veselin Topalov. One of his career highlights includes a notable game against Sergei Movsesian in 2006, where he produced a queen sacrifice which became one of the most celebrated chess moves of the year and symbolic of Navara's risky yet effective playing style.
His remarkable achievements are fuelled by an intense dedication to the game, often studying chess up to 30 hours a week. Despite his intense commitment, Navara maintains a modest and friendly demeanor, earning him popularity among other players. Amid his chess career, Navara also attended Charles University in Prague, studying both mathematics and logic. However, he faced challenges balancing both, leading to postponement of his studies to focus on his chess career. Apart from chess, Navara also has keen interests in classical music, reading classical literature, and solving logical puzzles.