  We review recent developments on the thermodynamics of black holes in
extended phase space, where the cosmological constant is interpreted as
thermodynamic pressure and treated as a thermodynamic variable in its own
right. In this approach, the mass of the black hole is no longer regarded as
internal energy, rather it is identified with the chemical enthalpy. This leads
to an extended dictionary for black hole thermodynamic quantities, in
particular a notion of thermodynamic volume emerges for a given black hole
spacetime. This volume is conjectured to satisfy the reverse isoperimetric
inequality - an inequality imposing a bound on the amount of entropy black hole
can carry for a fixed thermodynamic volume. New thermodynamic phase transitions
naturally emerge from these identifications. Namely, we show that black holes
can be understood from the viewpoint of chemistry, in terms of concepts such as
Van der Waals fluids, reentrant phase transitions, and triple points. We also
review the recent attempts at extending the AdS/CFT dictionary in this setting,
discuss the connections with horizon thermodynamics, applications to Lifshitz
spacetimes, and outline possible future directions in this field.
