Yefim Petrovich Geller was born on March 2, 1925 in Odessa.
Geller learned chess during World War II.
In 1946 Geller played in his first chess tournament and took 4th place in the Ukrainian Championship in Kiev.
In 1948 he graduated from Odessa University with a degree in political economy, but made chess his career.
He took 3rd-4th place in the 17th USSR championship in 1949. He was only a candidate master at the time and the lowest rated player.
In 1950 he won the Ukrainian championship and took 7th in the USSR Championship.
He took 2nd-3rd in the 1951 USSR championship.
His first international tournament was in Budapest in 1952. He took 2nd place (won by Keres), ahead of Botvinnik and Smyslov. He obtained the Grandmaster title in 1952. He took 4th place in the Stockholm interzonal in 1952.
He took 3rd place in the 1952 USSR championship.
In 1953 he took 6th place in the Zurich Candidates tournament.
He tied for first in 1955 USSR Championship with Smyslov, then defeated Smyslov in the play-off.
He took 5th place in the 1955 interzonal tournament in Goteborg.
He shared 3rd place in the 1956 Candidates tournament in Amsterdam.
In 1957 he won the Ukrainian championship.
In 1958 he won the Ukrainian championship.
In 1959 he won the Ukrainian championship.
In 1960 he took 2nd place in the USSR championship.
He tied for 2nd place in the 1962 Stockholm interzonal.
He tied for 2nd place with Keres in the 1962 Candidates tournament in Curacao. His peak Elo rating is estimated at 2655 from this event. He lost to Paul Keres in a match to qualify for the Candidates match.
In 1965 he took 1st place at Beverwijk. He lost to Smyslov in the Candidates quarter-final (Geller had replace Botvinnik).
In 1966 he took 2nd place in the USSR championship. He lost a match with Larsen in a Candidates match.
He tied for 2nd place in the 1967 Sousse interzonal.
In 1968 he took 1st place at Goteborg. He lost to Spassky in the Candidates quarter-final.
In 1969 he took 1st place at Wijk aan Zee.
In 1969 the first official FIDE rating listed Geller as 2620. Only 6 other grandmasters were rated higher than him: Fischer, Spassky, Korchnoi, Botvinnik, Petrosian, and Larsen.
He tied for 2nd place in the 1970 Palma de Majorca interzonal.
In 1971 he lost to Korchnoi in the Candidates quarter-final.
In 1973 he tied for 2nd in the Petropolis interzonal, but lost in a match-tournament with Portisch and Polugaevsky.
In 1975 he took 1st place at Teesside and at Moscow.
In 1976 he took 1st place at Las Palmas.
In 1976 he took 9th in the Biel interzonal.
In 1977 he took 1st place in the Hoogovens tournament in Wijk aan Zee.
In 1979 he won the USSR Championship at the age of 54. He won the USSR championship 24 years earlier.
In 1980 he tied for 1st at Las Palmas.
In 1982 he took 5th in the Moscow interzonal.
In 1984 he wrote APPLICATION OF CHESS THEORY.
He died of cancer on November 17, 1998 at the age of 73.