  We review developments in the theory of multiple, parallel membranes in
M-theory. After discussing the inherent difficulties pertaining to a maximally
supersymmetric lagrangian formulation with the appropriate field content and
symmetries, we discuss how introducing the concept of 3-algebras allows for
such a description. Different choices of 3-algebras lead to distinct classes of
2+1 dimensional theories with varying degrees of supersymmetry. We then
describe how these are equivalent to a type of conventional superconformal
Chern-Simons gauge theories at level k, coupled to bifundamental matter.
Analysing the physical properties of these theories leads to the identification
of a certain subclass of models with configurations of M2-branes in Z_k
orbifolds of M-theory. In addition these models give rise to a whole new sector
of the gauge/gravity duality in the form of an AdS_4/CFT_3 correspondence. We
also discuss mass deformations, higher derivative corrections as well as the
possibility of extracting information about M5-brane physics.
