This article describes recent developments in the understanding of the mechanism of enantioselection in one of the most efficient artificial catalytic reactions--Rh-catalyzed asymmetric hydrogenation. Numerous experimental and computational data are consistent with the idea that the enantioselection takes place through the reversible coordination of the double bond in octahedral dihydride complexes, which can happen only if the resulting chelate cycle is formed in the less hindered quadrant. In its main features, this mechanism of generating chirality resembles the recently uncovered three-stage recognition process occurring in enzymatic reactions.