The Medieval period lasted for a very long time. As social and political circumstances changed, the Pope’s fortunes shifted accordingly. For instance, the alliance between the Franks and the papacy was formed out mutual need. Charlemagne needed to legitimize his role as king, since the Franks were technically ruled by the Merovingian Dynasty (Although Charlemagne’s father and grandfather had ruled in fact, if not in name). The Pope needed protection from the Arian Lombards. Before the advent of the Catholic, Frankish military machine, it was not at all out of the question that a group like the Lombards could overwhelm the Papacy.

I’m not sure if this is exactly what you wanted to know. Could you be a bit more specific regarding time-period or type of power (military, political, cultural)? If you want a truly comprehensive overview, I've found Diarmaid MacCulloch’s Christianity: The First 3000 Years to be a wonderful resource.