This article focuses on a new concept in catalytic asymmetric synthesis, which was first realized by the use of heterobimetallic complexes. As such complexes function at the same time as both a Lewis acid and a Brønsted base, similar to enzymes, they make possible a variety of efficient catalytic asymmetric reactions. This “heterobimetallic” concept has proven to be applicable to a variety of new asymmetric catalyses. We have already succeeded in asymmetric nitroaldol reactions catalyzed by the LaLi₃tris (binaphthoxide) complex (LLB) and asymmetric Michael reactions catalyzed by the LaNa₃tris (binaphthoxide) complex (LSB). Now the LLB catalyst could also be applied efficiently to the tandem inter-intramolecular asymmetric nitroaldol reaction, affording a synthetically useful bicyclic product with four newly generated chiral carbons in one pot. Furthermore we succeeded in the first direct asymmetric aldol reactions of aldehydes with unmodified ketones (up to 94% ee) by using a catalytic amount of LLB. While LLB was also effective in the hydrophosphonylation of aldehydes, asymmetric hydrophosphonylations of imines were efficiently catalyzed by the LnK₃tris (binaphthoxide) complex (LnPB : Ln = rare earth metal such as La, Yb) (up to 96% ee). On the other hand, alkali metal free lanthanum complexes prepared from Ln (O-i-Pr) ₃ (Ln = La or Yb) and 1, 1'-binaphthol (BINOL) or 3- hydroxymethyl-BINOL were excellent catalysts for the asymmetric epoxidation of α, β-unsaturated ketones (up to 94% ee). We also developed another type of heterobimetallic catalysts featuring group 13 elements such as Al or Ga as a central metal. Among them, the AlLibis (binaphthoxide) complex (ALB) is an effective catalyst for asymmetric Michael reactions of malonates or Horner-Wadsworth-Emmons reagents (up to 99% ee) and for asymmetric tandem Michael-aldol reactions. Applications of this catalyst to syntheses of biologically important compounds such as 11-deoxy-PGF_1a, and tubifolidine are also described. Furthermore the GaLibis (binaphthoxide) complex (GaLB) in combination with molecular sieves 4 A was found to be an efficient catalyst for asymmetric ring openings of a variety of epoxides with t-BuSH (up to 97% ee).