Federalism and multilevel governance both emphasize polycentricity in governing arrangements. With their different intellectual pedigrees, these concepts are discussed in two separate sections. Fragments are now increasingly mixed up in hybrid forms of governance that also encompass originally unitary governments. All this results in a drift toward more substate regional authorities and the emergence of more informal, less state-dominated regulatory mechanisms. Accompanying processes of politicization and issues of legitimacy are explored. The EU and its predecessors are introduced as a site where federalism and multilevel governance have been proposed and turned down in spirited, politically charged discourse, using arguments made in the context of various social science disciplines.