Compactification of a stack of M5-branes on a non-trivial 3-manifold leads to a N=2 supersymmetric theory in 3 dimensions. If the 3-manifold in question is a knot complement, various Chern-Simons amplitudes - or corresponding knot invariants - for this knot determine the properties of the resulting 3d, N=2 theory. This relation between N=2 theories and Chern-Simons theory is referred to as the 3d-3d correspondence. M-theory realization of this correspondence implies, that N=2 theories obtained in this way posses one special flavor symmetry, which is related to certain refinement of Chern-Simons theory and the so-called homological knot invariants. In this talk I will discuss properties of these refined/homological invariants, and their role in the 3d-3d correspondence.