The people speaking Slav languages (a group within the Indo-European family) were converted to Christianity after the Church had split into two main parts: Catholic, based on Rome and western Europe; Orthodox, based on Constantinople (now Istanbul). Orthodox religion differs from the western (Roman) variety by: married priesthood (but celibate bishops); languages (Slavonic and Greek rather than Latin); distributed authority (no single Pope); ceremonial (read the theology books for details).

See wikipedia on the Slavic languages.

In Russia the Orthodox Church has become politically possible again, after being persecuted during the Communist period. It remains hostile to the missionary activity of western Catholics and Protestants and again has some influence over the government. In Serbia it has become the symbol of Serb Nationalism.

The 19th century Tsarist government of Russia professed solidarity with all the Orthodox peoples who had received their religion from the Byzantine Empire. Some of these also spoke Slav languages, with some degree of mutual intelligibility (but the first pan Slavic Congress of Prague in 1848 had to use German as a common language because the delegates could not in practice understand each other).

The motivation for the Tsar's policy was partly a desire to gain control of Constantinople (Istanbul) and to influence Bulgaria, Romania and Serbia. Possession of warm water ports in the Black and Mediterranean seas was another (Istanbul and Salonika).

Is this Orthodox sphere being recreated? It is hard to say. The Orthodox religion has gained in importance since the end of Communism but has not achieved the established condition it had under the Tsars (except perhaps in Greece). Russian interest in Serbia might be a sign of a new post-Communist expansion. Russian nationalists are using the Serbs as an excuse to reassert Russian interest and even hegemony.

In the Serbo-Croat speaking area of Yugoslavia the Orthodox religion is in fact the sign of a "Nation" - the Serbs - distinguishing them from the Catholic Croats. In Bulgaria it distinguishes the Slavs from the Muslim Turkish minority. In Greece it links the modern Greeks to their origin in the Byzantine Empire.

Non-Slav Orthodox are Romanians and Greeks (and Arabs in Lebanon, Palestine and Iraq).

Slavs
The western Slavs are Catholic. Poles, Slovaks and Slovenes are mostly Catholic, having been converted by missionaries from Rome. Czechs are partly Catholic and partly Protestant. Perhaps the main distinction is those Slav peoples who use the Cyrillic alphabet: Russians, Ukrainians, Byelorussians, Serbs and Bulgars and those who use the Latin alphabet: Poles, Slovenians, Croats, Czechs and Slovakians.

Further east the Sakartvelans (Georgians) are Orthodox but not Slavic. Armenians are not Orthodox, being Monophysite like the Ethiopians (but the Church and ritual look similar).
Does Orthodoxy produce autocracy in politics? Some of the most conservative apologists in Russia, such as Solzhenitsyn, argue in favor of dictatorship as long as it is not Communist or secular. Are Orthodox people intolerant? There is some evidence. The extreme nationalists in Serbia and Russia are often Orthodox. The Greek government and people are intolerant of linguistic and religious minorities.

New Cold War?
After Communism, will Orthodoxy become again the definer of the boundary between western and eastern Europe? If so, Greece is at present on the western side, though Orthodox. However, this division looks unlikely to produce any problems.

The border also passes through Ukraine, where the west is Catholic and Uniate, but the east is Orthodox. At the time of the ending of the Soviet Union some even said that a new Iron Curtain would pass through the center of Sarajevo. This does not seem to be the case.

These Orthodox states have joined the EU: Greece, Cyprus, Romania and Bulgaria.

Belarus and the Ukraine are ethnically part of the eastern Slav world of which the Russians are the dominant group. Nevertheless the religion of Rome penetrated as far as the western Ukraine which was at one time ruled by Lithuania-Poland. Russia itself was first influenced by Vikings (the Rus) then gained its first modern culture from Byzantium, was occupied by Muslim Tatars (part of the Mongol dispersion) and was long isolated from developments in western Europe. Thus the speakers of Russian have an ambiguous attitude to Europe, alternating between domination by westernizers and slavophiles. Gorbachov appeared to be a westernizer; Stalin has been considered a Slavophile; probably Putin, too.

Romania shares the same ambiguity. Its language comes from Rome; its religion and culture from Byzantium and Kiev. Bulgaria belongs to the same world of Orthodoxy and is always influenced by whatever the Russians are doing.

Ethiopia is sometimes considered Orthodox. However, its religion derives not from Byzantium but from Egypt and is Monophysite rather than Orthodox in theology.