He studied with Pyotr Stolyarsky in his native Odessa and after graduation from the Conservatory there he made his debuts in Moscow and Leningrad in his very early twenties. He was appointed a professor at the Moscow Conservatory in 1934 and his international career was launched when he won the Ysaÿe Competition in Brussels in 1937. The war interrupted this blossoming career, though Oistrakh continued to play, sometimes on the front lines for thousands of soldiers. After the end of hostilities Yehudi Menuhin played with Oistrakh in Moscow and news of this travelled to England very soon. His USA debut followed in 1955 with the Shostakovich 1st Concerto which was written for him.
After the war, through all the political ups and downs between East and West in the 1950s and 60s, Oistrakh continued giving concerts internationally at the top of his form. He was an ardent champion of his Soviet contemporary composers and so added to his already broad repertoire of concert and chamber works with their new compositions. Among others, Shostakovich, Prokofiev and Khachaturian wrote for him. He played chamber music with Lev Oborin and Vyacheslav Knushevitsky and gave countless recitals with Lev Oborin.