We review some recent computer modelling studies of grain boundaries in electroceramics. The paper focuses on rutile and zinc oxide which both have electronic device applications. The computational methodologies employed in these investigations, both classical and quantum mechanical, are described. Although the number of calculations is limited, there are indications that undoped symmetrical grain boundaries in rutile and zinc oxide are not electrically active whereas doped boundaries do exhibit interface states in the band gap which will influence the electrical properties of the material.