  Traditional treatments of the first law of black hole thermodynamics do not
include a discussion of pressure and volume. We give an overview of recent
developments proposing a definition of volume that can be used to extend the
first law to include these appropriately. New results are also presenting
relating to the critical point and the associated second order phase transition
for a rotating black-hole in four-dimensional space-time which is
asymptotically anti-de Sitter. In line with known results for a non-rotating
charged black-hole, this phase transition is shown to be of Van der Waals type
with mean field exponents.
