We present an analytical theory of vectorial wave coupling in photorefractive cubic crystals which are, in general, optically active. The theory is based on the systematic use of the spatial symmetry properties and the apparatus of the Pauli operators to deal with two-dimensional vectors and matrices. It allows one to give a unified description of a wide spectrum of photorefractive phenomena, including the efficiency and polarization properties of Bragg diffraction, polarization two-beam coupling enhanced by ac fields, the influence of the photoelastic effect, etc. Applications of the theory to crystals of the sillenite family and to particular photorefractive phenomena are given. A good qualitative agreement between the theoretical predictions and experimental data for Bi12TiO20 (BTO) crystals is shown.