AbstractThe theoretical and technical foundations are presented for the efficient relativistic electronic structure theories to treat heavy‐atomic molecular systems. This review contains two surveys of four‐component and two‐component quasi‐relativistic approaches. First, we review our highly efficient computational scheme for four‐component relativistic ab initio molecular orbital (MO) methods over generally contracted spherical harmonic Gaussian‐type spinors (GTSs). Illustrative calculations, which are performed with a new four‐component relativistic ab initio molecular orbital program package REL4D, clearly show the efficiency of our computational scheme by the Dirac–Hartree–Fock (DHF) and Dirac–Hartree–Fock (DKS) methods. Next, in the two‐component quasi‐relativistic framework, two relativistic Hamiltonians, RESC and higher order Douglas–Kroll (DK) Hamiltonians, are introduced, and several illustrative calculations are shown. Numerical results for several systems show that good accuracy can be obtained with our third‐order DK (DK3) Hamiltonian. © 2002 Wiley Periodicals, Inc. J Comput Chem 23: 847–860, 2002