This is a review of the elastic behaviour and pressure (P)-induced structural evolution of zeolites and presents a comparative analysis of the deformation mechanisms of the Si/Al-framework and the rearrangement of the extra-framework species in response to applied pressure. The interaction between P-transmitting fluids and zeolites, which can lead to phenomena such as ‘P-induced over-hydration’, is described. The comparative elastic analysis and the high-P structural data of zeolites reported so far allow us to make some generalizations: (1) The range of compressibility among this class of openframework silicates is large, with bulk moduli ranging between 15 and 70 GPa; (2) Microporosity does not necessarily imply high compressibility, as several zeolites are less compressible than other nonzeolitic rock-forming minerals; (3) Compressibilities of zeolites do not seem to be directly related to microporosity, at least if we model microporosity with the ‘framework density’; (4) The flexibility observed in zeolites under hydrostatic compression is mainly governed by tilting of rigid tetrahedra around O atoms that behave as hinges within the framework. Pressure-induced tilting commonly leads to continuous rearrangement of the framework without any phase transition. More rarely, tilting induces displacive phase transitions and isothermal P-induced reconstructive phase transitions (i.e. with change in framework topology), have not been reported in this class of materials; (5) Deformation mechanisms in response to applied pressure are generally dictated by the topological configuration of the framework rather than the Si/Al-distribution or the extra-framework content. The channel content governs the compressibility of the cavities, leading to different unit-cell-volume compressibilities in isotypic structures.