The ring-transformation reactions of three to five-membered heteroatom-containing saturated rings over porous materials are reviewed. As concerns the molecules, emphasis is placed on three-membered heterorings in general and epoxide derivatives in particular. However, typical features of the reactions of other saturated ring systems containing heteroatom(s) are also collected. As concerns the catalysts for these transformations, they are porous materials of various kinds: mainly small to large-pore molecular sieves, layered silicates, layered double hydroxides and miscellaneous porous substances (like Nafion-H, various forms of silica). From the reactant side the various types of ring transformations are discussed (isomerisation, heteroatom-loss, cyclic dimer formation, oligomerisation, etc.), activity and selectivity issues are described. From the catalyst side these reactions are related to the structure of the catalysts and the chemical nature of their active sites.