We construct three-dimensional Chern-Simons-matter theories with gauge groups $ U(N) \times U(N) $ and $ SU(N) \times SU(N) $ that have explicit $ \mathcal{N} = 6 $ superconformal symmetry. These theories are argued to describe the low-energy limit of $ N $ M2-branes probing a $ C^4/Z_k $ singularity. For large $ N $, the theory is dual to M-theory on $ AdS_4 \times S^7/Z_k $, and for the 't Hooft limit (large $ N $ with fixed $ N/k $), it is dual to type IIA string theory on $ AdS_4 \times CP^3 $. For $ k = 1 $, the theory is conjectured to describe $ N $ M2-branes in flat space, although only six of the eight supersymmetries are explicitly realized. The theory also has extra symmetries when the gauge group is $ SU(2) \times SU(2) $, making it identical to the Bagger-Lambert theory. The theories are analyzed in terms of their moduli space, chiral operators, and Wilson lines, and their gravity duals are discussed. The brane construction is lifted to M-theory, where it corresponds to M2-branes probing a transverse toric hyperkähler manifold, which has a singularity of the form $ C^4/Z_k $. The theories are shown to have an $ \mathcal{N} = 6 $ superconformal symmetry, and their moduli spaces are identified with those of M2-branes at the $ C^4/Z_k $ singularity. The theories are also shown to have an $ \mathcal{N} = 8 $ supersymmetry for $ k = 1 $ and $ k = 2 $, and their dual descriptions in string theory and M-theory are discussed.We construct three-dimensional Chern-Simons-matter theories with gauge groups $ U(N) \times U(N) $ and $ SU(N) \times SU(N) $ that have explicit $ \mathcal{N} = 6 $ superconformal symmetry. These theories are argued to describe the low-energy limit of $ N $ M2-branes probing a $ C^4/Z_k $ singularity. For large $ N $, the theory is dual to M-theory on $ AdS_4 \times S^7/Z_k $, and for the 't Hooft limit (large $ N $ with fixed $ N/k $), it is dual to type IIA string theory on $ AdS_4 \times CP^3 $. For $ k = 1 $, the theory is conjectured to describe $ N $ M2-branes in flat space, although only six of the eight supersymmetries are explicitly realized. The theory also has extra symmetries when the gauge group is $ SU(2) \times SU(2) $, making it identical to the Bagger-Lambert theory. The theories are analyzed in terms of their moduli space, chiral operators, and Wilson lines, and their gravity duals are discussed. The brane construction is lifted to M-theory, where it corresponds to M2-branes probing a transverse toric hyperkähler manifold, which has a singularity of the form $ C^4/Z_k $. The theories are shown to have an $ \mathcal{N} = 6 $ superconformal symmetry, and their moduli spaces are identified with those of M2-branes at the $ C^4/Z_k $ singularity. The theories are also shown to have an $ \mathcal{N} = 8 $ supersymmetry for $ k = 1 $ and $ k = 2 $, and their dual descriptions in string theory and M-theory are discussed.