The son of a musician who played in the military band in Siberian city of Krasnoyarsk, he showed an extraordinary musical talent at a very early age. In 1956 he entered Yuri Yankelevich's class at the Moscow Central School of Music, later entering the Moscow Conservatoire.
In 1966, at the age of 19 he won the first prize in the Third International Tchaikovsky Competition and was invited to appear on several international concert tours – something that had become much easier after the pioneering visits outside the Soviet Union by artists such as Richter, Gilels, Rostropovich, and Oistrakh. The influence of the last could be noticed in Tretyakov's interpretations and also in his choice of the repertoire; Tretyakov favoured the great romantic violin concertos such as those by Brahms, Mendelssohn, Tchaikovsky, Sibelius and music of Prokofiev and Shostakovich. His unique style is supported by impeccable technique and deep musical insight, created by an expressive use of phrasing.
Named a People's Artist of the USSR in 1987, Tretyakov was granted the Russian Prize for the encouragement of achievements in art and literature "Triumph". He is laureate of the Shostakovich Prize, awarded by the Yuri Bashmet International Charitable Foundation, and the Glinka State Prize of the RSFSR (1981) (other recipients include the Borodin Quartet and composer Valery Gavrilin), and recently was awarded "the Order of Service to the Fatherland" by President Vladimir Putin.
Since winning the International Tchaikovsky Competition in 1966, Tretyakov has performed with almost every major orchestra in the world, including Berlin, Vienna, Moscow, St. Petersburg, London, Los Angeles, and Munich Philharmonic Orchestras, the London Symphony Orchestra, the Philharmonia Orchestra, the Royal Philharmonic, Orchestre de Paris, Staatskapelle Dresden, Bamberg SO, NDR Hamburg, WDR Cologne, NHK Symphony, the Kirov Orchestra, the Concertgebouw Orchestra of Amsterdam, Bavarian Radio Symphony Orchestra, Vienna Symphony, and symphony orchestras of Chicago, Philadelphia, Cleveland, Atlanta, Detroit, San Francisco, Dallas, Pittsburgh, Toronto, and many others. He has worked with conductors including Rostropovich, Ormandy, Temirkanov, Alekseev, Jochum, Krips, Gergiev, Fedoseyev, Maazel, Kempe, Jansons, Järvi, Levine, Mehta, von Dohnanyi, Penderecki, Previn, and Kondrashin. He plays a 1772 Nicolo Gagliano violin.
For many years, Tretyakov has taught at the Moscow State Conservatory. In 1996, he took a teaching post in Cologne, Germany. From 1986 to 1994, he was the jury president of the International Tchaikovsky Competition. Additionally, he has served as a jury member of competitions in Brussels, Hanover, Sendai, Moscow, Helsinki, Zagreb, and many others. His notable students include Ilya Kaler, Natalia Likhopoi, Dmitri Berlinsky, Evgeny Bushkov, Sergei Stadler, and Daniel Austrich.
An active chamber musician, Tretyakov has performed together with Mstislav Rostropovich, Svyatoslav Richter, the Borodin Quartet, Oleg Kagan, David Geringas, Evgeny Kissin, and Elisabeth Leonskaja. Together with Vassily Lobanov, Yuri Bashmet, and Natalia Gutman, he has formed a piano quartet, in which he performs regularly. Their performances include concerts in Moscow, Berlin, Munich, Istanbul, Paris, Athens, Lisbon, and Copenhagen.