In this talk, I will present the theory of homological link invariants, together with some recent developments. The theory consists in categorifying various polynomial link invariants - like Jones, HOMFLYPT or Alexander polynomial - by defining the graded chain complexes whose homotopy type is the invariant of a link, and whose graded Euler characterstic is equal to the polynomial link invariants. I will show some basic constructions for the Jones polynomial (sl(2)-link invariant), so-called Khovanov homology, as well as its generalization for the HOMFLYPT polynomial (sl(n)-link invariant), so-called Khovano-Rozansky homology, and also some recent constructions of these homologies. If time permits, I will try to explain the knot Floer homology by Ozsvath and Szabo, which categorifies the Alexander polynomial.