In these notes, I will briefly describe the results which I will present in the talk entitled Cop and robber game and hyperbolicity, which are based on paper [3]. Generally speaking, our main result is that Gromov hyperbolicity can be characterized by the cop and robber game with speeds: in a ±-hyperbolic graph a slower cop can always catch a faster robber and, conversely, if in a graph G a slower cop can always catch a faster robber, then the hyperbolicity of G is quadratic in the speed of the cop. As a byproduct of our results, we obtain a constant factor approximation of hyperbolicity of an n-vertex graph in O(n2) time.