Take a look at this thread, as there are a few detailed comments there on what we know about the Slavs from the earliest literary sources (all of which place them in Eastern Europe close to the Danube River by the way) and the linguistic/archaeological evidence. There is very little information on why some Slavic peoples migrated or a consensus on how the Slavic identity developed however, so there's always room for more experts to add their input here :)

This doesn't answer your question fully, but according to Peter Heather's book "Empires and Barbarians: The Fall of Rome and the Birth of Europe", there are at least 8 different theories on the place of origin of the Slavs. This map shows the proposed homelands, together with a list of the historians who proposed them.

A follow-up question:

As an armchair student of Yugoslav history, most of the books I've read seem to agree that there was a massive influx of Slavs into the Balkans in the sixth century: thousands of them in a short span of time, who all but subsumed the Illyrians and other pre-Slavic peoples. (Either by war, displacement or cultural integration). This doesn't square with the belief that the Slavic migrations were piecemeal or a slow evolution.

Any Slavic experts care to comment?