JSJ decompositions of finitely generated groups are a fundamental tool in geometric group theory, encoding all splittings of a group over a given of subgroups. We give a unified account of this theory with complete proofs and many examples. We introduce a simple and general definition of JSJ decompositions, the natural object being a deformation space of actions on trees, similar to Outer Space. In many cases of interest, this deformation space contains a canonical JSJ tree, which is invariant under automorphisms.