I will discuss recent joint work with Ben Elias, in which we develop a combinatorial method for computing the triply graded homology (equivalently, the superpolynomial) of certain links, especially torus links. Conjecturally, this link homology has deep connections with Hilbert schemes and symmetric functions. For instance the superpolynomial of the $(n,nk)$ torus link is conjecturally an evaluation of $nabla^k (p_1)^n$. I will discuss some evidence for this conjecture, including recent work of Andy Wilson.