Some theoretical methods for description of the diffusion on modulated surfaces are reviewed. A general formula for calculation of the diffusion coefficient of a particle moving in the field of a periodic potential is developed, which takes into account both the potential barrier effect and the dependence of the friction coefficient on the potential. The application of the theory to the diffusion of dimers on solid surfaces reveals a non-monotonous dependence of the diffusion coefficient on the ratio between the dimer and solid spatial parameters. This resonant dependence sometimes can be suppressed by the rotations and vibrations on the dimer. In the present theory the latter are described via an adiabatic approach.