As soon as the Moscow Virtuosi were formed, the ensemble was called from all over the world. they have toured in Europe, America, Asia, performing in countries such as Great Britain, France, Germany, United States, Japan, etc.

For several years the Moscow Virtuosi were not allowed to perform in the United States due to the broken diplomatic relations between the USSR and the USA. Finnaly, in 1987 they made their debut in the United States with such success that they returned in 1989 for a twenty-four-concert tour, and have regularly come back every year to perform in the most important halls both in the States and Canada.

Since 1989, the Moscow Virtuosi, with Vladimir Spivakov as conductor, regularly attend the Music Festival of Marbella (Spain), Rheingau Musik Festival in Wiesbaden (Germany), Scheslig Holstein Musik Festival (Germany), Festpiele Wiltz Festival (Luxemburg) and Festival Internationale de Colmar (France) where they give not only concerts but also masterclasses.

They perform in the most world-famous halls such as Carnegie Hall and Avery Fisher in New York, Davies Orchestra Hall in San Francisco, Chicago's Symphony Orchestra's hall in Chicago, Boston Symphony Orchestra's hall in Boston, Concertgebouw in Amsterdam, Champs-Elysées in Paris, Auditorio Nacional in Madrid, Palau de la Música in Barcelona, Opera Theatre in Frankfurt, Barbican Hall in London, Rome, Montecarlo, Japan. They also participate in the following series: Greatest Orchestras of the World (Madrid) and Greatest International Events (Mexico).

Since August 1989, BMG/RCA Victor Red Seal has published twenty-two CDs with the Moscow Virtuosi and Vladimir Spivakov frequently accompanied by other great soloists such as Mikhail Rudy, Evgenij Kissin, Natalie Stutzman, Michala Petri, etc.

Now that the Moscow Virtuosi Chamber Orchestra has become an independent society established in Asturias (Spain) since 1990, it began a new episode in which it will not only follow the previous success but will also open new perspectives and try to widen its cultural project towards new objectives but keeping the seal of its musical excellence, being specially relevant the inclusion of twelve of its solists in the main string stands of the recently created Orquesta Sinfónica Ciudad de Oviedo (OSCO) and their participation in the "magistralia" music courses organised by Fundación Magistralia.