We review developments in the theory of multiple, parallel membranes in M-theory. After discussing the inherent difficulties with constructing a maximally supersymmetric lagrangian with the appropriate field content and symmetries, we introduce 3-algebras and show how they allow 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 demonstrate that these theories are equivalent to conventional superconformal Chern-Simons gauge theories at level. k, but with bifundamental matter. Analysing the physical properties of these theories leads to the identification of a certain subclass of models with configurations of M2-branes on. Zk orbifolds. These models give rise to a whole new gauge/gravity duality in the form of an. AdS4/CFT3 correspondence. We also discuss mass deformations, higher derivative corrections, and the possibility of extracting information about M5-brane physics.
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