I will introduce a family of supersymmetric Chern-Simons-matter theories in d=2+1 dimensions, labelled by a positive integer n, and argue using a number of different dual descriptions that these describe the worldvolume dynamics of M2-branes at a corresponding family of four-fold hypersurface singularities (the n=1 theory being the ABJM theory). The IR properties of these theories and their deformations are also studied.