The classical Bishop-Gromov's inequality concerns Riemannian manifolds whose Ricci curvature is bounded below. We shall recall briefly its proof and some of its consequences: Gromov's precompactness Theorem and the upper bound on the first Betti number. We may briefly mention the generalisation to metric spaces whose synthetic Ricci curvature is bounded below. We shall then focus on metric measured spaces satisfying a weak doubling property, in particular to Gromov-hyperbolic metric spaces. This leads to a finiteness theorem on Gromov Hyperbolic groups satisfying some natural conditions. This talk is intended to be a survey adapted to graduate students. This is a joint work with G. Courtois, S. Gallot and A. Sambusetti.