  Quasifuchsian hyperbolic manifolds, or more generally convex co-compact
hyperbolic manifolds, have infinite volume, but they have a well-defined
``renormalized'' volume. We outline some relations between this renormalized
volume and the volume, or more precisely the ``dual volume'', of the convex
core. On one hand, there are striking similarities between them, for instance
in their variational formulas. On the other, object related to them tend to be
within bounded distance. Those analogies and proximities lead to several
questions. Both the renormalized volume and the dual volume can be used for
instance to bound the volume of the convex core in terms of the Weil-Petersson
distance between the conformal metrics at infinity.
