In the present review we give an account of dielectric studies under high pressure on plastic and liquid crystalline phases. We emphasize the usefulness of employing hydrostatic pressure as an important parameter for varying the average inter-molecular distance. Furthermore high-pressure studies are indispensable in order to establish the equation of state and the phase diagram for the substance under investigation, let alone that a wealth of phase transitions is only observed at elevated pressures. In the Introduction we outline the basic concepts of mesophases, dielectric theories and experimental procedures. The essential part of the review deals with the presentation of dielectric results for plastic and liquid crystals under high pressures. Both the static and complex permittivity is treated. The latter yields the dielectric relaxation time whose temperature and pressure dependence enables us to derive the activation enthalpy and activation volume, respectively. The dielectric properties of some cyclic and branched alcohols are compared with previous work on the various ice phases. Recent high-pressure studies on some nematic liquid crystals are presented and discussed. The review also briefly notes other dielectric studies under high pressure in neighbouring fields.