  We present the gauged N=4 (half-maximal) supergravities in four and five
spacetime dimensions coupled to an arbitrary number of vector multiplets. The
gaugings are parameterized by a set of appropriately constrained constant
tensors, which transform covariantly under the global symmetry groups SL(2) x
SO(6,n) and SO(1,1) x SO(5,n), respectively. In terms of these tensors the
universal Lagrangian and the Killing Spinor equations are given. The known
gaugings, in particular those originating from flux compactifications, are
incorporated in the formulation, but also new classes of gaugings are found.
Finally, we present the embedding chain of the five dimensional into the four
dimensional into the three dimensional gaugings, thereby showing how the
deformation parameters organize under the respectively larger duality groups.
