  The strong sphaleron rate, i.e., the rate of real time QCD topological
transitions, is a key phenomenological quantity, playing a fundamental role in
several physical contexts. In heavy-ion collisions, a non-vanishing rate can
lead to the so-called Chiral Magnetic Effect. In early-Universe cosmology,
instead, it can be related to the rate of thermal production of QCD axions. In
this talk, we present the first reliable fully non-perturbative computation of
the strong sphaleron rate in $N_f=2+1$ QCD at the physical point by means of
lattice simulations, in a range of temperatures going from 200 MeV to 600 MeV.
Our strategy is based on the inversion of lattice correlators via a
recently-proposed modified version of the Backus-Gilbert method.
