He won many international tournaments in Eastern Europe during his career, and tied for the Soviet Championship title in 1963, but lost the playoff.

Kholmov stayed active in competitive chess right to the end of his life, and maintained a high standard of play past the age of 80.

He served as a sailor in the Soviet merchant marine during World War II, sailing mainly the Northern Arctic route.

Later that year, he made his first high-level appearance at the Mikhail Chigorin Memorial, Moscow 1947, scoring 5½/15 against a powerful international field.

Kholmov qualified for his first Soviet final in 1948, Moscow URS-ch16, scoring 8½/18 for 12th place, where the winners were David Bronstein and Alexander Kotov.

At Moscow URS-ch17, 1949, he showed solid improvement, finishing tied 9th–10th with 10/19, as Bronstein and Vasily Smyslov won.

Kholmov made his international debut at Bucharest 1954 with a tied 3rd–4th place, on 11/17, as Viktor Korchnoi won.

In the URS-ch26 at Tbilisi 1959, Kholmov continued his improvement at the top Soviet level with a tied 4th–5th place, with 12/19, as Tigran Petrosian won.

Kholmov won at Kecskemét 1962 with 11/15, ahead of Lajos Portisch and László Szabó, who tied for 2nd–3rd places.

Consequently, Kholmov is arguably the strongest player of the era ranging from the 1940s through the 1960s to never hold the title of Soviet Champion.

Then Kholmov suffered perhaps his greatest career disappointment in the Soviet Zonal tournament, Moscow 1964, where he scored 6/12 for 4th in a super-strong field, but fell one place short of advancing to the Interzonal stage.

He made a notable result at Havana 1965 with 5th place on 14½/21, as Smyslov won, but Kholmov defeated Bobby Fischer and finished undefeated in the tournament.

His form in his late 40s had substantially fallen from his best years, and a new generation of Soviet players would earn most of the top tournament places and international opportunities.

One of Kholmov's best late-career results was his tied 3rd–5th place in a very strong Moscow 1975 tournament, with 9½/15, as Geller won.

Kholmov tied for the title in the 2000 World Senior Championship at Rowy, on 8/11 with Mark Taimanov, Jānis Klovāns, and Alexander Chernikov.

Kholmov was known as "The Central Defender"[1] in Soviet chess circles, because of his great skill at repulsing enemy aggression.

Kholmov was comfortable as White with both 1.e4 and 1.d4, could play excellent classical chess with both colours, and had an occasional fondness for unusual openings, with which he had good success, as the game selection shows.