The asymmetric catalytic hydrogenation of olefins is one of the most widely studied and utilised transformations in asymmetric synthesis. This straightforward and atom-economical strategy can provide excellent enantioselectivity for a broad variety of substrates and is widely relevant for both industrial applications and academic research. In many instances the hydrogenation is stereospecific in the regard that the E–Z-geometry of the olefin governs the stereochemistry of the hydrogenation, producing an enantiodivergent outcome. Interestingly, the possibility to hydrogenate E- and Z-isomer mixtures to a single stereoisomer in an enantioconvergent manner has been reported. This avoids the need for synthesis of geometrically pure alkene starting materials and therefore constitutes a significant practical advantage. This review article aims to provide an overview of the different stereochemical outcomes in the hydrogenation of olefins. Although the field is well developed and selectivity models have been proposed for a number of catalytic systems, an organized collection of enantioconvergent results, as opposed to the more common enantiodivergent case, might promote new investigation into these phenomena.