The Quartet made its debut in 1965, and began intensive work in 1968. In 1972 it was awarded the highest prize in the international string quartet competition in Lieges, Belgium, being renamed after Lithuania's capital city the following year.

The quartet has toured in over 30 countries, and has given over 2500 concerts. Currently (2003) it is performing around 80 concerts per year, in Europe, Africa, Central And South America and Asia, including many major festivals, and is drawing international praise for its technique and interpretation skills.

The quartet has a vast repertoire of over 400 works, including all the classics, but also over 100 works by contemporary composers, many of which have been written especially for them.

The quartet is in high demand owing to its high artistry, and has recorded over 30 albums around the world.