  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 is a major contributor to the error of the
theoretical prediction as described in the recent white paper [1]. We have
shown 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 $g-2$.
