The term Russian Chant refers to a group of chant traditions used by the Church of Russia and some of its daughter churches, both monophonic and polyphonic, representing influences from multiple sources, both traditionally Orthodox as well as Western. Russian chant is used not only in the Church of Russia, but also in the Churches of Ukraine, Finland, Japan, the OCA and elsewhere.
Probably the earliest distinctive variety of chant in use in the regions that came to be known as Russia is Znamenny Chant, a traditionally monophonic (i.e., melodic, non-harmonized) chant derived ultimately from the Byzantine Chant brought to the Rus' by Greek missionaries sent from Constantinople.
Western-style harmonizations eventually came into use in the Russian church via Lvov and Kiev due to the influence of the Roman Catholic Church from Poland, and polyphony "suddenly burst into Russian liturgical singing from the West in the middle of the seventeenth century" (Johann von Gardner, Russian Church Singing, Vol. I: Orthodox Worship and Hymnography, p. 380). In the mid-18th century, the choirmasters of the imperial court were mainly Italians, which further pushed Russian church music in a Western direction. In the 19th century, German composition principles came to dominate in Russian chant.
In the Russian church today, these various traditions all remain in use throughout the church as well as in its daughter churches, some in more primitive form than others. There is currently a revival underway in some monasteries and parishes of use of the more ancient forms of chant, particularly Znamenny.
One peculiar element of Russian chant is the group of traditions known in Russia as "Greek Chant" and "Bulgarian Chant." While the origins of both are a matter of some debate, neither variety of chant is something characteristic of the use of either the Greek or Bulgarian churches, which primarily use Byzantine and Bulgarian chant, respectively.