The work of Alexandrov and Ranninger has shown that the extrapolation of the BCS theory to strong electron-phonon interaction necessarily involves the formation of small polarons. The resulting theory can be directly applied to the cubic bismuth oxides, in which the bosons are Bi³⁺, existing both above and below T_c. In the copper oxide materials, the role of the spins in Cu²⁺ is discussed. A model is proposed in which both spin and dielectric polarons play a role. The model is applied to electrical properties above T_c, for under- and over-doped specimens, and various other phenomena.