This short review provides an overview as well as background of ongoing work in our laboratory on unconventional catalysts in selective oxidation reactions with remarkable selectivity. The three cases reviewed here have in common that the catalysts are oxides that do not posses any formal redox capacity. The use of doped defective oxides gives rise to surface-redox chemistry in the case of partial oxidation of methane over yttrium-modified zirconia, where actual removal of oxygen from the surface sites indeed takes place. Surprisingly, this oxygen species is not able to activate hydrogen to a significant extent. In contrast, Li-modified MgO catalyst does not allow removal of oxygen; O¿ sites generated by Li are now able to abstract a H-radical from, e.g., propane. Radical gas-phase chemistry of the propyl radicals is then responsible for selective formation of olefins. The significant fact in this case is that olefins are activated to a lesser extent then alkanes. The remarkable selectivity obtained in propane oxygenation on earth-alkali-modified zeolite Y at unusually low temperatures is due to the confinement of radicals in the cages of the zeolite, turning radical chemistry into stoichiometric chemistry. The second significant effect is the very effective stabilization of the resulting oxygenate, acetone, in the cage. However, the stabilization thus also implies extremely strong adsorption of the acetone, thus preventing desorption of the product. Our work indicates that desorption can be assisted by offering water as a competitive adsorbing species, thus opening the possibility to close the catalytic cycle.