Enantioselective aliphatic C-H bond oxidation simultaneously installs functionality and chirality into hydrocarbon units, converting in a single step readily available, inexpensive and typically inert hydrocarbons into precious building blocks for organic synthesis. The reaction remains however an open problem eager for catalyst development and improvement. Metal complexes reproducing structural and reactivity aspects of oxygenases are emerging as promising homogeneous catalysts for this class of reactions. The present work reviews the current status of field, analyzing the difficulties of the reaction, discussing principles of catalyst design, and critically highlighting the limitations of the current state-of-the-art methodologies.