A review of both dense and porous ceramic membranes for high temp. oxidn. reactions, i.e. partial and total oxidns. Non-permselective porous membranes are efficient contactors for total oxidn. of VOC or soot. They are also still attractive as oxygen distributors for the partial oxidn. of long chain alkanes, although dense mixed conducting membranes are now on the way to be commercialized for methane involving reactions. By a proper selection of the ion conducting materials compn., structure and thickness, and by combining in a suitable way both dense and porous layers, the oxygen flux, performance and stability of dense ceramic membranes can be considerably improved. In view of the large no. of material challenges and scientific approaches found in the literature, it is clearly difficult to be exhaustive. New developments in the field of advanced membranes constantly contribute to improve the potential of membrane reactors, through the development of new prepn. methods, of optimized layer stacking and of new membrane materials with original or improved properties. After a rapid overview on both dense and porous membranes used for oxidn. reactions, examples of the developments in the field of membrane materials, structures, architectures, synthesis methods and reactor designs are reported, coming from either the authors Institute or from the recent literature on both membrane reactors and SOFCs.