Mstislav Rostropovich and Galina Vishnevskaya met in 1955 at the "Prague Spring" festival. They married that same year, four days after meeting, marking Vishnevskaya's third marriage. The couple remained married for 52 years, from 1955 until Rostropovich's death in 2007.
The pair frequently performed together on international stages, with Rostropovich acting as a pianist and conductor for Vishnevskaya. Rostropovich conducted the opera "Eugene Onegin" for Vishnevskaya's farewell performance at the Paris Opera in October 1982.
In September 1969, they offered their dacha as a residence to Aleksandr Solzhenitsyn and wrote an open letter in his support in October 1970. In 1974, the couple and their children left the Soviet Union. In March 1978, they were deprived of their Soviet citizenship and awards while living abroad in the United States and France. Their citizenship was restored in 1990.
They had two daughters, Olga (born 1956) and Elena (born 1958). The couple established the "Vishnevskaya–Rostropovich" foundation, which engages in medical charity and children's vaccination. Following Vishnevskaya's death in 2012, she was buried next to her husband at the Novodevichy Cemetery in Moscow.