Canonically, Western Rome 'falling' in 476 (end of Antiquity) and the shift of Latin to Greek as the administrative language of the Eastern Roman Empire by the end of the 7th century, following the Arab conquests & the loss of their eastern provinces (end of Late Antiquity). All in all, these are arbitrary pickings. They don't necessarily correspond to major events in reality. More significant than Odoacar deposing the last Western Roman Emperor is, for example, the establishment of the Carolingian Empire, or prior to this the Renovatio Imperii of Justinian and the ensuing Justinian Plague.

You'd need to define "medieval". For some of us in its broader European terms it's the 5th-15th centuries or thereabouts (in which case not much happened between the first-named episode and the later period, because one begins the other, although of course it's never as straightforward as that); for some though it's a narrower period, e.g. the 11th-15th centuries (though even the 14th-15th centuries sit uneasily alongside the preceding "high middle ages"), in which case you'd be asking about what used to be labelled the "dark ages" and the Carolingian and subsequent period.

For the period immediately following Rome's fall (which only ended the western empire, the eastern surviving for another millennium) in the west is the ongoing migration of Germanic peoples into former Roman territory and the establishment of regional kingdoms under various forms of social organisation that would in time evolve into "feudal", manorial or seigneurial hierarchical ties of obligation underpinned spiritually by the spread of Latin Christianity. In eastern Europe it's the survival and temporary recovery of the eastern or Byzantine empire and the westward movement of Slavs, Magyars and others. Along the way we get the revival of money in the west (silver far more importantly than gold), trade and towns, though the big growth comes from the 10th century.

For most of the world, the periodisation's of course largely meaningless, and different start and end dates have to be used for any parallel concept. Even in Europe it's a shorthand, but a useful one provided we're aware of its limitations and the lack of unanimity over even what period's being referred to.