  Considering de Rham-Gabadadze-Tolley theory of massive gravity coupled with
(ghost free) higher curvature terms arisen from the Lovelock Lagrangian, we
obtain charged AdS black hole solutions in diverse dimensions. We compute
thermodynamic quantities in the extended phase space by considering the
variations of the negative cosmological constant, Lovelock coefficients
($\alpha_{i}$) and massive couplings ($c_{i}$), and prove that such variations
is necessary for satisfying the extended first law of thermodynamics as well as
associated Smarr formula. In addition, by performing a comprehensive thermal
stability analysis for the topological black hole solutions, we show in what
regions thermally stable phases exist. Calculations show the results are
radically different from those in Einstein gravity. Furthermore, we investigate
$P-V$ criticality of massive charged AdS black holes in higher dimensions,
including the effect of higher curvature terms and massive parameter, and find
that the critical behavior and phase transition can happen for non-compact
black holes as well as spherically symmetric ones. The phase structure and
critical behavior of topological AdS black holes are drastically restricted by
the geometry of event horizon. In this regard, the universal ratio, i.e.
$\frac{{{P_c}{v_c}}}{{{T_c}}}$, is a function of the event horizon topology. It
is shown the phase structure of AdS black holes with non-compact (hyperbolic)
horizon could give birth to three critical points corresponds to a reverse van
der Waals behavior for phase transition which is accompanied with two distinct
van der Waals phase transitions. For black holes with spherical horizon, the
van der Waals, reentrant and analogue of solid/liquid/gas phase transitions are
observed.
