A significant result from research on the influence of hydrostatic pressure on the dielectric properties of compositionally disordered ABO 3 perovskites has been the discovery of a pressure-induced ferroelectric(FE)-to-relaxor (R) crossover making the R state, the ground state, of these materials at reduced volume. This crossover appears to be a general phenomenon that we have studied in a variety of different systems. Here we discuss results on PMN, PSN, PZN-9.5PT and PLZT 6/65/35 to illustrate various aspects of the phenomenon on different materials. We also discuss the interplay between the effects of pressure and dc biasing field on the dielectric response and phase behavior. While pressure favors the R state, biasing fields favor the FE state. The combined results provide new insights into the physics and can be explained in terms of changes in the correlation length for dipolar interaction among the polar nano-regions (PNRs) that exist in these disordered materials.