  The properties of the QCD axion are strictly related to the dependence of
strong interactions on the topological parameter theta. We present a
determination of the topological properties of QCD for temperatures up to
around 600 MeV, obtained by lattice QCD simulations with 2+1 flavors and
physical quark masses. Numerical results for the topological susceptibility,
when compared to instanton gas computations, differ both in size and in the
temperature dependence. We discuss the implications of such findings for axion
phenomenology, also in comparison to similar studies in the literature, and the
prospects for future investigations.
