Given a non-elementary random walk on the isometry group of a Gromov hyperbolic space, we can consider the hitting measure on the Gromov boundary. The regularity of this hitting measure depends on the moment condition on the random walk. In this talk, I will review Benoist and Quint’s approaches to the log-regularity of the hitting measure. I will then explain the improvement of this theorem using the recently developed theories of Gouëzel and Baik-Choi-Kim. If time allows, I will discuss its generalization to other settings, i.e., the CAT(0) visual boundary and the sublinearly Morse boundary.