A federation is a large, often multi-ethnic, state originally based on mutual agreement between the participants. Compare with Empire, a term describing a large, multi-ethnic state, whose political structure was originally put together by coercion.

In Australian history, "federation" refers to the formation of the Commonwealth of Australia by six British colonies on 1 January 1901, and also to the political movement in the 1890s to bring this about.

Examples of states which are or claim to be federations:

Some countries exhibit characteristics of a federation, but are not. For example, Spain has a relationship resembling that of a federation with its autonomous communities; however, they are created by and exist at the suffrance of the central government, rather than being distinct entities that have chosen to join together. Same for Belgium.

The Russian Federation is also not a true federation. It consists of Russia proper, which includes the great majority of the population and is governed by the national government in Moscow, and a number of small ethnic enclaves known as Autonomous Republics or Autonomous Oblasts, but these enclaves have little real autonomy.

It is arguable that the European Union has some of the attributes of a federal state, although its member states are separate entities under international law, unlike the more traditional examples above. The EU could move towards being a genuine Federation if its character were to evolve from the current confederal, Community structure to decision-making on a federal basis.

In Star Trek, a collection of science fiction works, the Federation is short for United Federation of Planets.