535.4:548The evolution of the theoretical and experimental background for a photorefractive effect in cubic gyrotropic piezocrystals is reviewed. It is shown that the impact of the inverse piezoelectric effect and the photoelasticity on the formation and properties of holograms recorded in such crystals is not reduced to minor quantitative variations in their output characteristics but gives rise to qualitative changes both in the orientation and polarization dependences of the hologram diffraction efficiency and in the gain of an object wave at the expense of a reference one. Contributions of various scientific optical schools to the development of theoretical and experimental investigations on the photorefractive effect in cubic piezoelectric crystals are acknowledged and the importance of the experimental results is demonstrated. Particular emphasis is placed on ways to optimize the output characteristics of holograms recorded in cubic gyrotropic photorefractive piezocrystals. Among these are the choice of crystal cut, the selection of the crystal orientation, and the polarization of the light waves.