This is a talk about the physical perspective on knot invariants of the homological type. Starting with knots decorated with the fundamental representation of sl(N), I will review the basic motivation, some mathematical definitions, and the relations with BPS invariants and topological strings on the resolved conifold. I will then present the conjectural extension of the theory to a larger class of Lie algebras and representations, and interrelations between them. This is joint work with Sergei Gukov.