Non-zero mass is compatible with unbroken gauge invariance in three spacetime dimensions (3D). A systematic procedure for the construction of massive gauge theories will be illustrated by new massive gravity, which propagates unitarily two massive spin 2 modes in a Minkowski vacuum. The supergravity extension of this model will be presented along with new results on supersymmetric AdS vacua. The extension to a new N=8 3D supergravity will be discussed, as will be the AdS3CFT2 correspondence and possible connections to string/M-theory.