Asymmetric catalysts ("chemzymes") for abiological transformations are complementary to natural enzymes for biological transformations. Thus, the development of asymmetric catalysis by chiral metal complexes for abiogenetic-type reactions, carbon-carbon bond formations in particular, is the most challenging and formidable endeavor for synthetic organic chemists. Described herein are the recent developments of highly enantioselective catalysis by a chiral binaphthol-derived titanium complex for the carbonyl-ene reactions which involve carbonyl compounds as the enophiles. The striking features of the titanium catalysis are also disclosed which include the positive nonlinear effect (asymmetric amplification) and the asymmetric desymmetrization. 1. Introduction 2. Asymmetric Catalysis for Carbonyl-Ene Reactions 3. Asymmetric Catalytic Glyoxylate-Ene Reaction 3.1. Role of Molecular Sieves 3.2. Positive Nonlinear Effect (Asymmetric Amplification) 4. Asymmetric Catalytic Diels-Alder Reaction 4.1. Hetero-Diels-Alder Reaction with Glyoxylate 4.2. Diels-Alder Reaction 5. Asymmetric Desymmetrization 5.1. Asymmetric Catalytic Desymmetrization 5.2. Kinematic Resolution and Double Asymmetric Induction 6. Ene Cyclization 6.1. Asymmetric Catalytic Ene Cyclization 6.2. Desymmetrization in Ene Cyclization