I discuss the set of rates of growth of a finitely generated
group with respect to all its finite generating sets. In a joint work
with Sela, for a hyperbolic group, we showed that the set is
well-ordered, and that each number can be the rate of growth of at most
finitely many generating sets up to automorphism of the group. I may
discuss its generalization to acylindrically hyperbolic groups.
