This paper gives an overview of the materials transport processes which occur in oxide solid electrolytes subjected to a generalized thermodynamical potential gradient. The general equations allowing to describe the transport processes on the anionic and cationic sublattices are given. Kinetic demixing processes and microstructural changes leading to surface instabilities are analysed. Experimental results obtained with yttria-doped zirconia and gadolinium doped ceria illustrate the importance of these phenomena on the transport properties of the materials but also on their long term stability in operating conditions.