David Bronstein was born in Bila Tserkva, Ukrainian SSR, Soviet Union, to Jewish parents. Growing up in a poor family, he learned chess at age six from his grandfather. As a youth in Kiev, he was trained by the renowned International Master Alexander Konstantinopolsky. He finished second in the Kiev Championship when he was only 15, and achieved the Soviet Master title at age 16 for his second-place result in the 1940 Ukrainian SSR Chess Championship, behind Isaac Boleslavsky, with whom he became close friends both on and off the chessboard. His first wife was Olga Ignatieva one of the strongest female chess players of the 1950s. He later went on to marry Boleslavsky's daughter, Tatiana, in 1984.

After completing high school in spring 1941, his plans to study mathematics at Kiev University were interrupted by the spread of World War II throughout eastern Europe in the early 1940s. He had begun play in the 1941 semifinal of the Soviet Championship, but this event was cancelled as war began. Shortly after the war's conclusion, he began attending Leningrad Polytechnical Institute where he studied for approximately one year.

Judged unfit for military service, Bronstein spent the war performing various jobs; this included doing some reconstruction of war-damaged buildings and other clerical/labor type jobs. Also during the war, his father, Johonon, was unfairly imprisoned for several years in the Gulag and was detained without substantial evidence of committing any crimes, it was later revealed.^[1] The rumor that Bronstein was related to the former Soviet Communist leader Leon Trotsky (whose real family name was Bronstein), was treated as unconfirmed, but doubtful, by Bronstein in his book The Sorcerer's Apprentice (1995). This belief could have explained the imprisonment of Bronstein's father.

With the tide turning towards an eventual Soviet war victory over the Nazi invaders, Bronstein was able to once again play some competitive chess. His first top-standard Soviet event was the 1944 USSR Championship, where he won his individual game against eventual winner (and soon-to-be world champion) Mikhail Botvinnik. Bronstein moved to Moscow as the war wound up. Then seen as a promising but essentially unproven young player, one of dozens in the deep Soviet vanguard, he raised his playing level dramatically to place third in the 1945 USSR Championship. This result earned him a place on the Soviet team; he won both his games played on board ten, helping the Soviet team achieve victory in the famous 1945 US vs. USSR radio chess match. He then competed successfully in several team matches, and gradually proved he belonged in the Soviet chess elite. Bronstein tied for first place in the Soviet Championships of both 1948 and 1949.

Bronstein's first major international tournament success occurred at the Saltsjöbaden Interzonal of 1948, which he won. His qualifying place in this event came through nominations from foreign chess federations. He earned his Grandmaster title in 1950, when FIDE, the World Chess Federation, formalized the process. His Interzonal win qualified him for the Candidates' Tournament of 1950 in Budapest. Bronstein became the eventual Candidates' winner over Boleslavsky in a (Moscow) 1950 playoff match, following two overtime match games, after the two had tied in Budapest, and then again remained level over the 12 scheduled match games.

The period 1945–1950 saw a meteoric rise in Bronstein's development, as he reached the World Chess Championship challenge match, in 1951.

Bronstein is widely considered to be one of the greatest players not to have won the World Championship.^[2] He came close to that goal when he tied the 1951 World Championship match 12–12 with Mikhail Botvinnik, the reigning champion. Each player won five games, and the remaining 14 games were drawn.

In a match where the lead swung back and forth several times, the two players tested each other in a wide variety of opening formations, and every game (except the 24th) was full-blooded and played hard to a clear finish. Bronstein often avoided lines he had favoured in earlier events, and frequently adopted Botvinnik's own preferred variations. This strategy seemed to catch Botvinnik by surprise; the champion had not played competitively for three years since winning the title in 1948. The quality of play was very high by both players, although Botvinnik would later complain of his own weak play. He only grudgingly acknowledged Bronstein's huge talent.^[3] Bronstein claimed four of his five match wins by deep combinational play, winning before adjournment in highly complex fashion. He led by one point with two games to go, but lost the 23rd game and drew the final (24th) game. Under FIDE rules, the title remained with the holder, and Bronstein was never to come so close again.

Botvinnik wrote that Bronstein's failure was caused by a tendency to underestimate endgame technique, and a lack of ability in simple positions.^[4] Botvinnik won four virtually level endgames after the adjournments, and his fifth win came in an endgame that Bronstein resigned at move 40. These adjourned games made up four of Botvinnik's five match wins; Botvinnik had no more than a minimal advantage in these games when they were adjourned at move 40.

Bronstein's father was sometimes secretly in the audience during the 1951 title match games, at a time when he was not officially permitted in Moscow.^[5]

Bronstein challenged throughout at the 1953 Candidates Tournament in Switzerland and finished tied for second-through-fourth places, together with Paul Keres and Samuel Reshevsky, two points behind the winner Vasily Smyslov. Bronstein's book on the tournament is considered a classic.

It has been speculated that there was pressure on the Soviet players to collude, to ensure that a Soviet player would win. Even in the wake of glasnost, however, Bronstein only partially confirmed these rumors in his public statements or writings, admitting only to 'strong psychological pressure' being applied, and that it was up to Bronstein himself whether to decide to give in to this pressure. In his final book Secret Notes, published in 2007, shortly after his death,^[6] Bronstein went further and alleged that he and Keres were pressured to draw their games with Smyslov, in order to ensure that Smyslov would win ahead of Reshevsky (see World Chess Championship 1954 § Allegations of Soviet collusion).

The 1953 Candidates result qualified him directly for the 1955 Gothenburg Interzonal, which he won with an unbeaten score. From there it was on to another near miss in the 1956 Candidates' tournament in Amsterdam, where he wound up in a large tie for third through seventh places, behind winner Smyslov and runner-up Keres.

Bronstein had to qualify for the 1958 Interzonal, and did so by placing third at the USSR Championship, Riga, 1958. At the 1958 Interzonal in Portorož, Bronstein, who had been picked as clear pre-event favourite by Bobby Fischer, missed moving on to the 1959 Candidates' by half a point, dropping a last-round game to the much weaker Filipino Rodolfo Tan Cardoso, when the electrical power failed due to a thunderstorm during the game, and he was unable to regain concentration. Bronstein missed qualification at the Soviet Zonal stage for the 1962 cycle. Then at the Amsterdam 1964 Interzonal, Bronstein scored very well, but only three Soviets could advance, by a FIDE rule, and he finished behind countrymen Smyslov, Mikhail Tal, and Boris Spassky, who finished as the joint winners, along with Larsen. His last Interzonal was at age 49 when he finished sixth at Petropolis 1973.

Bronstein took many first prizes in tournaments, among the most notable being the Soviet Chess Championships of 1948 (jointly with Alexander Kotov) and 1949 (jointly with Smyslov). He also tied for second place at the Soviet Championships of 1957 and 1964–65. He tied first with Mark Taimanov at the World Students' Championship in 1952 at Liverpool. Bronstein was also a six-time winner of the Moscow Championships, and represented the USSR at the Olympiads of 1952, 1954, 1956 and 1958, winning board prizes at each of them, and losing just one of his 49 games in those events. Along the way he won four Olympiad team gold medals. In the 1954 team match against the US (held in New York), Bronstein scored an almost unheard-of sweep at this level of play, winning all four of his games on second board.

Further major tournament victories were achieved at Hastings 1953–54, Belgrade 1954, Gotha 1957, Moscow 1959, Szombathely 1966, East Berlin 1968, Dnepropetrovsk 1970, Sarajevo 1971, Sandomierz 1976, Iwonicz Zdrój 1976, Budapest 1977, and Jūrmala 1978.