Sergei Vasilyevich Rachmaninoff was born in Russia to a musical family and started learning the piano from a young age. He start composing as a teenager, studied initially at the St. Petersburg Conservatory and then graduated from the Moscow Conservatory in 1892. Most of his compositions were composed and performed in Russia where he was influenced by Russian composers such as Tchaikovsky and Mussorgsky. Some of Rachmaninoff's early works received critical acclaim. However the premier of his First Symphony was something of a disaster, resulting in poor reviews from music critics. The composer took it badly and suffered from depression, and it was several years before he composed his 2nd symphony which was better received. After the Russian revolution of 1917 during which his family estate at Ivanovka was vandalised he left the country with his family initially for Scandinavia, but with war spreading across much of Europe he then moved to the United States (where he had already gained some popularity after touring the country). In the US he was primarily based in New York City and refocussed his career as a pianist and conductor earning a living as a recording artist and touring celebrity. He met many other musicians and became friends with Vladimir Horowitz, another Russian pianist who settled in the US. Because of his performing career his output as a composer slowed considerably during this period, but he still managed to compose some of his best work (helped by a brief relocation to Switzerland) including his 3rd Symphony and his "Rhapsody on a Theme of Paganini". Back in the US during WWII and in declining health he moved to the warmer climate of California in 1942 but died the following year shortly after becoming an American citizen.
Although he lived well into the 20th century, in terms of compositional style Rachmaninoff is best described as a Late Romantic composer. His music often sounds Russian and the influence of Russian composers such as Tchaikovsky, Mussorgsky, Rimsky-Korsakov and Balakirev is clear. The Romanticism of his sound is also clear in some of the lushly scored melodies of his Symphonies and Concertos. His Piano Concerto No.2 composed in 1901 became especially popular and it was used in the film "Brief Encounter" in 1945 (expertly played by Australian pianist Eileen Joyce), and later it formed the basis of the song "All by Myself" by Eric Carmen (who also borrowed Rachmaninoff's music in the song "Never Gonna Fall in Love Again"). These romantic and nostalgic qualities undoubtedly helped to secure his popularity among listeners, although the downside is that his popularity (and traditional style) was initially looked down upon in the world of classical music. However Rachmaninoff's reputation as a composer is now very much intact with his mastery of counterpoint particularly evident, and even his First Symphony is now better regarded. Despite his "late romantic" label there are aspects of Rachmaninoff's music which push into the Modern era, such as his complex harmonies and chromaticism, and the bold way in which he adapted established forms.
A few years before "Brief Encounter" Rachmaninoff was asked by the makers of the film "Dangerous Moonlight" to write a concerto-like piece. When the composer declined the job fell to Richard Addinsell who then wrote the "Warsaw Concerto". However Rachmaninoff's music plays a significant role in other films. The famous 18th Variation from his "Rhapsody on a Theme of Paganini" plays a key role in the film "Somewhere In Time", and Bill Murray's character in "Groundhog Day" uses his endless time to also learn this 18th Paganini Variation to impress his love interest. In the film "Shine" (based on true events), the pianist David Helfgott enters a Piano Competition and chooses to play the difficult 3rd Piano Concerto. In addition to his legacy as a composer, Rachmaninov left a number of paper rolls and recordings which (desite their being from an early period of recording technology) demonstrate his talents as a pianist.
Rachmaninoff composed a number of purely orchestral works including a total of 3 symphonies. However he is best known for his piano works, both those for solo piano and also those for piano and orchestra such as his Piano Concertos and his famous Rhapsody on a Theme of Paganini. His piano music is regarded as difficult to play (with one of the difficulties arising from his legendary big hands) but is now very much part of the concert repertoire.
Here are some recommended recordings of Rachmaninoff's music: