- Arguably the world's best cellist, he was also Music Director of the National Symphony in Washington, DC, for 17 years, and toured extensively as a cellist and internationally acclaimed orchestra conductor and pedagogue.
- Awarded the Polar Music Prize, the Royal Swedish Academy of Music Award, in 1995.
- Longtime friend of writer Aleksandr Solzhenitsyn. In 1969 Rostropovich saved the dissident writer Aleksandr Solzhenitsyn from prosecution.
- Music director of the National Symphony Orchestra, in Washington D.C., from 1977 to 1994.
- Very close friends with composers Dmitri Shostakovich, Sergei Prokofiev and Benjamin Britten. They each wrote concert works for him to play as a cellist.
- Fled the Soviet Union in 1974 with his wife and two daughters, Olga and Elena. Their citizenship was revoked by Leonid Brezhnev in 1978. In 1990, Mikhail Gorbachev restored their citizenship of Russia (then Soviet Union).
- Founded the Vishnevskaya-Rostropovich Foundation to help to improve the health care of children in former Soviet lands in 1991.
- His father and grandfather were both cellists.
- Made his concert debut at the age of 13.
- Played his cello at the Berlin Wall when it came down in November 1989 and played the Bach Unaccompanied Cello Suites amidst the rubble.
- Honors include: Recipient of Order of Service to the Fatherland medal of Russia (2007). Honorary Knight Commander of the British Empire, a Commander of the Legion of Honor of France, a Commander of the Phoenix Order of Greece, holder of the Commander's Cross of the Order of Merit of the Federal Republic of Germany, Presidential Medal of Freedom, Kennedy Center Honoree, the State Stalin's Prize (1951), the title People's Artist of the USSR (1956), and the Defender of Free Russia Medal (1993).
- Recipient of U.S. Presidential Medal of Freedom in 1987 and a knighthood conferred on him that year by Queen Elizabeth II on his 60th birthday.
- Studied at the Moscow Conservatory, after beginning the cello at age 7.
- Buried at Novodevichy Convent Cemetery in Moscow.
- Has two daughters, Olga and Elena.
- Played a Stradivari cello named Duport Stradivarius.
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