  In this review articel we study the gaugings of extended supergravity
theories in various space-time dimensions. These theories describe the
low-energy limit of non-trivial string compactifications. For each theory under
consideration we review all possible gaugings that are compatible with
supersymmetry. They are parameterized by the so-called embedding tensor which
is a group theoretical object that has to satisfy certain representation
constraints. This embedding tensor determines all couplings in the gauged
theory that are necessary to preserve gauge invariance and supersymmetry. The
concept of the embedding tensor and the general structure of the gauged
supergravities are explained in detail. The methods are then applied to the
half-maximal (N=4) supergravities in d=4 and d=5 and to the maximal
supergravities in d=2 and d=7. Examples of particular gaugings are given.
Whenever possible, the higher-dimensional origin of these theories is
identified and it is shown how the compactification parameters like fluxes and
torsion are contained in the embedding tensor.
