This paper summarizes some advances achieved in the first 10 years of studies on nanosized ionic and mixed conductors. It addresses first concepts: boundary core and space charge effects, impedance and percolation models. Then, some consensual evidence is presented: nanocrystals show no particular structural disorder and their electrical conductivity can be nicely interpreted using space charge theory, as shown for the model case of nanosized ceria. However, there are also controversial cases, such as doped zirconia, for which very different results were reported. Finally, concerns on long-time stability of nanosized solids are addressed. Recent studies of phase stability and grain growth show that these issues might be overcome. (c) 2006 Elsevier B.V. All rights reserved.