Chiral metal-organic frameworks (CMOFs) have shown great promises in the applications of asymmetric catalysis with highly enantioselective. Herein, we briefly overview recent processes of MOF-based asymmetric catalysts based on a classification of reaction types. And we mainly focus on the structures and compositions of the active sites in these catalysts and their performances in specific reactions. In addition, some of their important unique features are critically emphasized alongside. Challenges of the future research are discussed also at the end of this review.