Chant development in the Eastern Church was clearly built on the musical norms that came into the Christian Church from Greek culture. It appears that the earliest example we have of Christian music composed in classical Greek meter is a work of Clement of Alexandria, and it seems to imitate common metrical poetry in style. According to Egon Wellesz, this hymn "shows how the master of the Catechetical school tried to combine the spirit of Greek poetry with Christian theology."  The dependence upon Greek musical theory, meter and form is further illustrated by what is probably the earliest Christian musical document we have, the Oxyrhynchus Hymn to the Holy Trinity. This document (Papyrus 1786) contains words and music dating from the end of the third century. The lyrics are in Greek, and the notation used is classical Greek vocal notation.
After Constantine's edict of toleration, and the legalization of Christianity which allowed (in fact required) it to develop a more public demeanor, music began to develop in formal ways. These musical types almost certainly were based on classical Greek theory and practice, although they were now coming to be called "Byzantine" after the new capitol of the Empire. In the coming centuries the development of liturgical chant blossomed in parallel with the theological and worship development of the Church.
The adoption of the eight modes of Greek music allowed Byzantine music to develop and convey specific feeling (such as sorrow or joy) that could correspond with the liturgical cycle. During this same period, some of the greatest composers in the history of the Eastern Church created glorious music and contributed new musical forms to the Church. The Church honored these composers, such as Ephraim the Syrian, Andrew of Crete, Joseph the Hymnographer, Kosmas the Poet, John Damascene, and Romanos the Melode, by enrolling them among the saints. 
During this same period, other forms of Eastern chant developed, such as Armenian, Georgian, Maronite, etc. Most were practiced in the non-Chalcedonian churches (those not subscribing to the Council of Chalcedon, and therefore considered non-Orthodox) and this allowed their continuation. For the Byzantine Church, liturgical music, like the liturgical rite itself, became standardized at a fairly early time.
As Eastern or "Greek" Christianity spread through its missionary efforts, so did the use of the vernacular language. When in 862 Sts. Cyril and Methodius (brothers from Thessaloniki, Greece) undertook missionary efforts in Slavic lands (Moravia), they were chosen and sent by Patriarch Photius, and brought with them Byzantine chant. The period of their ministry was rife with political and ecclesiastical tension in the Slavic countries, and at one time resulted in an appeal to Pope Hadrian regarding the question of liturgical language. Cyril and Methodius received the Pope's blessing to continue the use of Greek. One of the long term outcomes of their work was the creation of an alphabet to allow the translation of Scripture and liturgical texts into the vernacular language.
As the Slavic lands, and last of all Rus, adopted Christianity, most also initially adopted Byzantine chant. Over time, however, these new cultures contributed their own musical heritage and cultural elements, thereby developing chant forms uniquely their own. For instance, among the earliest chant forms in the history of Russian Orthodoxy is Znamenny Chant. It is a very "Byzantine sounding" chant from which used a different notation system and included distinctively Russian musical elements. Kievan chant, another early Russian chant form, likewise developed.
A variety of other minor chant forms developed in the history of the Russian church, but the most notable changes in Russian Orthodox chant development came with the reforms of Peter the Great. Peter imported musicians from Western Europe and undertook a major change in the musical form of Russian liturgical music. The result is the unique ambience and feeling of Russian Orthodox music, in contrast to Byzantine chant.
The following pages provide overviews of specific areas of interest in the chant development of the Eastern Orthodox Church.