Computational methods for the analysis of transition metal complexes have undergone rapid progress in the recent past. Improved methods, most notably effective core potentials including relativistic correlations, new methods for determining analytic first and second energy derivatives and efficient methods for obtaining multiconfiguration wavefunctions, have been developed. Combined with new computational technologies, most notably the development of parallel hardware and software, this provides exciting new opportunities to investigate quantitatively the bonding, structure and reactivity of complexes incorporating transition metals from the entire series. This review covers recent work from our laboratories, in which all of these emerging technologies have been used. Subjects to be discussed include the nature of multiple bonds between transition metals and main group elements and the activation of prototypical bonds by transition metals. We focus on multiply bonded transition metal-main group (TM=MG) complexes of the early transition metals, because of the vigorous experimental research that has been done in this area, particularly as it pertains to catalysis and advanced materials applications. The bonding and structure of alkylidene (L(n)M=C(R)R'), silylidene (L(n)M=Si(R)R') and imido (L(n)M=NR) complexes are reviewed. Some recent results on oxo (L(n)M=O), sulfido (L(n)M=S) and phosphinidine (L(n)M=PR) complexes are also presented. Bonding is, in general, interpreted using the language of valence bond theory, made possible by the development of localization methods for multiconfigurational orbitals. This approach is quite useful, since it conforms to the language used by the experimental community in their analyses of the bonding and reactivity of TM=MG complexes, yet it retains the fundamental molecular orbital approach. Of particular interest are the following questions. (1) Can a computational scheme be developed to predict accurately the properties of experimentally characterized TM=MG species, thus allowing confidence in studies of TM=MG complexes whose reactivity is not conducive to X-ray structural analysis? (2) For a given L(n)M, how does the basic picture of metal-ligand multiple bonding change from alkylidene to imido to ore, and from silylidene to phosphinidene to sulfide? (3) What are the essential features of the potential energy surfaces relating to bond activation? (4) How do TM=MG species involving the heavier elements (MG=Si, P and S) compare with their lighter congeners? (5) Are any trends in the properties of the transition metal-main group linkage discernible (as a function of M, L(n) or E), which may provide new insight into the reactivity of these complexes in the various important processes in which they participate, and which may help to design more effective TM=MG materials through modification of the chemical environment?