Early writing in the Slavic languages is traditionally attributed to Saint Cyril (also called Constantine) and his brother Saint Methodius, two missionaries sent to Bulgaria from Greece in the 9th century who invented a Slavic alphabet with which they could translate liturgical texts. Early Slavic writing is attested in both the Glagolitic and Cyrillic scripts, although the exact origins and derivation of each of these are not known for certain.
It is apparent that Glagolitic writing predates Cyrillic writing. Some believe Glagolitic to be an original creation, but the general consensus is that it was based on cursive Greek letters, with possible borrowing from Coptic and Armenian. Some early Slavic documents suggest that Glagolitic writing may have existed before Saints Methodius and Cyril arrived in the area, and that the brothers merely systemized the existing script.
The origins of Cyrillic are a little clearer. The shapes of many letters are clearly based on the upper case Greek letters, and those which are not may be traced to Glagolitic. Also inherited from Greek was the assignment of a numerical values to each letter. Early forms of the script were unicameral, that is, having only one case.
Early sources do not refer to two separate alphabets, nor use either of the names by which we now know these scripts. However, documents from the time confirm that they were used in tandem until the 13th century, when the Cyrillic script became dominant. During this period, the Glagolitic script, despite being the earlier system, was influenced by the Cyrillic script in that the shapes of some letters changed.
The Glagolitic script continued to be used in Croatia until the early nineteenth century; elsewhere it was gradually supplanted by the Cyrillic script.
Cyrillic was confined to Bulgaria, Serbia and Russia until the 19th century.
By the 1980s the area encompassed by the Soviet Union contained approximately 60 written languages. Some of these were written in the Latin script, others in Arabic. Some, for example Georgian and Armenian, used a script unique to that language. However, as Cyrillic became more associated with the Soviet regime, all of these languages came to be written in Cyrillic, either exclusively or alongside their previous script.
Due to the various sound systems the script had to transcribe, some modifications were made in the way it was used by different languages. As a result, not all languages use the same set of symbols, and some languages assign different phonetic values to a given sign. For example, Г represents [ɣ] in the Belarusian and Kabardian alphabets, [ɦ] in Ukranian and [g] in Bulgarian, Abkhaz and Uzbek, and alternates [g] and [ʁ] in Kirghiz and Tatar writing.
Paul Cubberley "The Slavic Alphabets" in The World's Writing Systems, Daniels & Bright (eds.) 346-355