Continuing rapid advances both in computer hardware and theoretical methodologies are enabling significant growth in the application of computational methods in the field of Transition Metal (TM) chemistry. This review provides a broad summary of the major types of model currently used to examine the geometries, electronic structures and reactivities of single-centre TM systems. It is aimed at iaorganic chemists in general rather than at the specialist theoreticians. The typical properties one might wish to calculate and the methods available are surveyed and the computational aspects discussed emphasising the special needs of TM species. Selected applications are then reviewed to assess the level of accuracy that can presently be anticipated and to provide a pointer to those methods worthy of further investigation.