Geller's first notable result was sixth place in the 1947 Ukrainian SSR Chess Championship at Kiev with 9½/15; the winner was Alexei Sokolsky.

Geller began to make his mark in the late 1940s, as he won the USSR Championship semifinal qualifier at Tbilisi 1949 with 11½/16, thus advancing to the final later that year.

His finals debut was sensational at URS-ch17 at Moscow; as a virtual unknown he tied for 3rd–4th places with 12½/19, behind only winners David Bronstein and Vasily Smyslov.

Geller defeated such established players as Semyon Furman, Isaac Boleslavsky, Alexander Kotov, Salo Flohr, fellow finals debutant Tigran Petrosian, Viacheslav Ragozin, and Grigory Levenfish.

Despite this showing, he was obliged to return to the semifinal level the next year, but advanced with a third-place finish in the 1950 qualifier at Kiev with 9/15.

Geller in 1950 made his international debut at the Przepiorka Memorial at Iwonicz Zdroj with 11½/19 for seventh place in a powerful field; Keres won again.

Geller played in 23 USSR Chess Championships, a record equalled by Mark Taimanov, achieving good results in many.

He returned to the interzonal stage in 1970 at Palma de Mallorca, and qualified as a Candidate again, losing his first match to Korchnoi at Moscow by 5½–2½.

In 1973, he tied with Lajos Portisch and Lev Polugaevsky for second place at the Petropolis Interzonal, but lost out in the three-way playoff match tournament at Portorož, with two qualifying spots at stake, so he did not advance.

Geller had an overall plus score against four world champions: Mikhail Botvinnik +4−1=7, Vasily Smyslov +11−8=37, Tigran Petrosian +5−3=32, Bobby Fischer +5−3=2.

[4] In total, Geller played ten and beat eight world chess champions, and his overall record in games in classical chess against world champions is positive: +39−36=131 (Max Euwe +1−1, Mikhail Botvinnik +4−1=7, Vassily Smyslov +11−8=37, Mikhail Tal +6−6=23, Tigran Petrosian +5−3=32, Boris Spassky +6−10=22, Bobby Fischer +5−3=2, Anatoly Karpov +1−2=5, Garry Kasparov +0−1=2, Viswanathan Anand +0−1=1).

Geller is best remembered today for the tactical ability and original attacking style which characterised the earlier part of his career.

He was noted as an openings expert, and was one of the pioneers in developing the King's Indian Defence to prominence, along with fellow Ukrainians Isaac Boleslavsky and David Bronstein.