After a brief introduction on ongoing experimental and theoretical activities on $(g-2)_\mu$, I will describe recent progress in approaching the calculation of the hadronic light-by-light contribution with dispersive methods. I will discuss general properties of the four-point function of the electromagnetic current in QCD, its Lorentz decomposition and dispersive representation. Based on these I will then present our numerical estimate for the pion box contribution and its rescattering corrections. I will conclude with an outlook for this approach to the calculation of hadronic light-by-light.