In this talk recent progress in studying the short-distance properties of the hadronic light-by-light contribution to the muon $g-2$ is described. The intermediate and short-distance part contributes a large part of the error of the theoretical prediction as described in the white paper. We showed that the massless quark-loop is the first term in a systematic expansion at short-distances, a result already used in the white paper. Newer results conclude that both nonperturbative and perturbative corrections are under control. The talk describes these developments and how they fit in the total theoretical prediction for the muon $g-2$.