Materials displaying high oxide-ion and/or proton conductivity have been attracting considerable interest for application as electrolytes in solid oxide fuel cells. In this respect, materials with the fluorite or perovskite-type structures have traditionally been targeted, but there is now growing interest in new structure-types. Important aspects to address are the dominant defects and mechanism of ionic conduction in such systems, and in this paper we highlight the benefits of a combined experimental and computer modelling approach to the investigation of such systems. With reference to recent work on apatite-type Ln9.33+x(Si/GeO4)6O2+3x/2, gallate-based Ln1-xBa1+xGaO4-x/2, and cuspidine-type Ln4(Ti2-xGaxO8-x/2)O2 (Ln=rare earth) we discuss the conduction mechanisms in these systems, showing the importance of co-operative effects in the conduction process.