  We study the $P-V$ criticality and phase transition in the extended phase
space of charged Gauss-Bonnet black holes in anti-de Sitter space, where the
cosmological constant appears as a dynamical pressure of the system and its
conjugate quantity is the thermodynamic volume of the black hole. The black
holes can have a Ricci flat ($k=0$), spherical ($k=1$), or hyperbolic ($k=-1$)
horizon. We find that for the Ricci flat and hyperbolic Gauss-Bonnet black
holes, no $P-V$ criticality and phase transition appear, while for the black
holes with a spherical horizon, even when the charge of the black hole is
absent, the $P-V$ criticality and the small black hole/large black hole phase
transition will appear, but it happens only in $d=5$ dimensions; when the
charge does not vanish, the $P-V$ criticality and the small black hole/large
phase transition always appear in $d=5$ dimensions; in the case of $d\ge 6$, to
have the $P-V$ criticality and the small black hole/large black hole phase
transition, there exists an upper bound for the parameter
$b=\widetilde{\alpha}|Q|^{-2/(d-3)}$, where $\tilde {\alpha}$ is the
Gauss-Bonnet coefficient and $Q$ is the charge of the black hole. We calculate
the critical exponents at the critical point and find that for all cases, they
are the same as those in the van der Waals liquid-gas system.
