Many federal states have a division of powers between the national, regional and local levels, or the national and supra-national levels in the case of international federations.
Some powers (competences) rest with the federation, others with the participating Member States. There may also be “mixed” or "shared" competences and rules to determine who will control these “shared” competences.
The future
The EU Constitution contains a catalogue of competences:
Links
See Categories of competence and Convention working groups.