  A classical result of J\o rgensen and Thurston shows that the set of volumes
of finite volume complete hyperbolic $3$-manifolds is a well-ordered subset of
the real numbers of order type~$\omega^\omega$; moreover, each volume can only
be attained by finitely many isometry types of hyperbolic $3$-manifolds.
  Fujiwara and Sela established a group-theoretic companion of this result: If
$\Gamma$ is a non-elementary hyperbolic group, then the set of exponential
growth rates of~$\Gamma$ is well-ordered, the order type is at
least~$\omega^\omega$, and each growth rate can only be attained by finitely
many finite generating sets (up to automorphisms).
  In this talk, we outline this work of Fujiwara and Sela and discuss related
results.
