One of the twentieth century's greatest violinists, Leonid Kogan conceived a fascination for the violin by age three. At six, he began lessons with Philip Yampolsky, a pupil of Leopold Auer. When his family moved to Moscow when he was ten, he began studies with Abram Yampolsky. He progressed through the Central School of Music, then the Moscow Conservatory, where he trained from 1943 to 1948. Postgraduate studies at the conservatory occupied him from 1948 until 1951.

At age 12, Leonid Kogan was heard by violinist Jacques Thibaud, who predicted a great career for him. Although his parents resisted exploiting their son as a prodigy, he made his debut at 17 and performed in many Soviet venues while still a student. Wider recognition came when Kogan shared first prize at the 1947 Prague World Youth Festival. In 1951, he won first prize at the Queen Elisabeth Competition. David Oistrakh, who was a member of the jury (along with Thibaud), thereafter came to regard Kogan as a colleague, while Kogan closely observed his elder associate during the latter's evening classes for other students.

After teaching at the Moscow Conservatory and playing a busy schedule of concerts in the Soviet Union over the next few years, Kogan made his first appearances in Paris and London in 1955, following those with a tour of South America in 1956 and another of the United States in 1957. After being named People's Artist in 1964, Kogan received the Lenin Prize in 1965.