Rostropovich was widely considered the world's greatest cellist during his lifetime. He recorded nearly the entire cello repertoire, and inspired many famous composers to create works especially for him, including Shostokovich and Prokofiev. He was also a leading conductor, a pianist, and a well-known and dedicated defender of human rights, most notably in his outspoken defense of writer Alexander Solzhenitsyn.

Both his parents were musicians—his mother was a pianist and his father a cellist who studied with Pablo Casals. His father began teaching him when he was only three, and he gave his first performance at eight. When he was 16 he entered the Moscow Conservatory, and in 1945 he won the gold medal in the first ever Soviet Union competition for young musicians. He became a professor of cello in 1956 and in 1968 debuted as a conductor. In 1977 he became music director of the National Symphony Orchestra in Washington, D.C., and held that position until 1994. He continued to appear as a cellist and conductor around the world until his death at age 80.