Black holes and Boyle's law -- the thermodynamics of the cosmological constant

When the cosmological constant, $\mathrm{\Lambda }$, is interpreted as a thermodynamic variable in the study of black hole thermodynamics a very rich structure emerges. It is natural to interpret $\mathrm{\Lambda }$ as a pressure and define the thermodynamically conjugate variable to be the thermodynamic volume of the black hole (which need not bear any relation to the geometric volume). Recent progress in this new direction for black hole thermodynamics is reviewed.