The design of efficient and general methods for the selective oxyfunctionalization of unactivated carbon-hydrogen bonds continues to represent a major challenge for the community of chemists, despite the fact that the oxidation of alkanes is a major feature of the chemical economy. A low level of selectivity is characteristic of large-scale oxidation of hydrocarbons performed under customary industrial oxidizing conditions (e.g., the catalytic air oxidation of cycloalkanes); in these processes, selectivity is difficult to control, because they are often impacted by the usual problems associated with free-radical chain reactions. Thus, in the last decades much work has been devoted to the search for general methods of selective oxidation that could be applied to a variety of satured hydrocarbons. In this context, just a few leading methods appear encouraging at the present time. This Account addresses a new approach developed in our laboratory, consisting in the application of isolated dioxiranes, a class of powerful yet selective oxidants. We contend that the method shows promise to contribute resolution of a well-recognized general problem in the existing chemistry of alkanes, that is, to achieve efficient oxyfunctionalizations with high selectivity for simple as well as structurally complex targets.