In the past decade, the asymmetric Morita-Baylis-Hillman (MBH)/aza-Morita-Baylis-Hillman (aza-MBH) reaction has attracted great attention because it leads to the formation of densely functionalized products in a catalytic and atom-economic way. The MBH/aza-MBH adducts can be further applied in a wide variety of organic synthesis, such as peptide synthesis and heterocyclic compounds synthesis. After a lot of attempts to improve the enantioselectivity, many types of chiral organocatalysts have been identified as highly enantioselective organocatalysts in MBH/aza-MBH reaction. Especially, certain "privileged chiral catalysts" are highly enantioselective in MBH/aza-MBH reaction, which are designed and developed through introducing bi-/multi-functional groups on the so-called "privileged structures" such as cinchona alkaloids, BINAP/BINOL. This review summarizes the exciting advances about the design and development of chiral catalysts derived from "privileged structures" and their applications in asymmetric MBH/aza-MBH reaction.