In this brief review recent progress in the application of computer simulation techniques to the thermodynamics and diffusion processes in highly nonstoichiometric materials is discussed. For the discussion of thermodynamics we review the application of the Monte Carlo method and its recent full integration with lattice relaxation methods. For the discussion of diffusion we also review the application of the Monte Carlo method with special emphasis on concentrated as well as defective systems and also its integration with lattice relaxation methods. Testing of relations among phenomenological coefficients, tracer diffusivities and ionic conductivities is also commented on.