Abstract: In the present paper a brief review is given of the historical development in valence bond (VB) theory,The mathematical formulation of the symmetric group approach for VBtheory is summarized,and some important approaches to modern valence bond theory,such as the spin-coupled VB (SCVB),generalized VB(GVB),and VBself-consistent-field(VBSCF)approaches are briefly reviewed.Optimization methods for one electron orbitals are discussed:fully optimized overlap-enhanced orbitals (OEOs)would probably yield an excellent VBwave function, even with only a single covalent structure, but would obscure theclassical interpretation,On the other hand,the use of bonded-distorted orbitals (BDOs)provides a clear classical description in terms of an interplay between covalent and ionic structures,Special attention is given to the bonded tableau unitary group approach (BTUGA),a spin-free VBmethod:an effective algorithm for evaluating Hamiltonian andoverlap matrices is presented,and an ab initio nonorthogonal VBcalculation programme is introduced;Furthermore,the BTUGAapplications are extensivelv reviewed,which include resonance energy calculations,discussions of molecular structures, potentical energy surface calculations, discussion of electron transfer in molecules,studies on the excited states,and the influence of orbital hybridization on single bond lengths.

Key words: Morden valence bond theory, Bonded tableau approach, Resonance theory, VBSCF, Ab initio