In recent years, the computational method Density Functional Theory (DFT) has become more and more important as an effective tool for studying inorganic complexes. This thesis describes computational studies on ruthenium polypyridyltype complexes using DFT. An introduction to the theory behind DFT is presented in the first chapter, as well as a review of previous DFT studies on ruthenium polypyridyl-type complexes. The second chapter describes the details of the computational studies. This includes a description of the basis set, functional, and integration grid. This chapter also describes two pieces of in-house software: GaussSum written to process the output of the computational package Gaussian, and GauStock, which is used to calculate Hirshfeld atomic charges. Chapter 3 examines the electronic structure of a series of complexes related to [Ru(bpy)2(pytrz)]+. The calculated electronic structure is compared with results from experiment. Partial density of states (PDOS) spectra are used to visualise the results. Linkage isomerism and methylation reactions are examined using thermodynamics and, in the case of methylation reactions, also with kinetics. Chapter 4 compares the electronic structure of dinuclear complexes with their corresponding mononuclear analogues. PDOS spectra are used to highlight the changes that occur on addition of a second metal centre. The quality of the predicted Raman frequencies of [Ru(bpy)3]2+ is the focus of Chapter 5. The effect of basis set size, grid size and the inclusion of solvent effects is discussed. The results are compared with the experimental values. Chapter 6 presents the first DFT study of an osmium complex attached to a surface, in this case, to a gold (111) surface. A cluster model is used for the surface. The effect of adsorption on the energy levels of the complex is studied. The effect of oxidation on the adsorbate-substrate bond is also examined. Chapter 7 is an overview of the information available from DFT calculations. DFT is a very useful tool for examining the electronic structure of ruthenium polypyridyl complexes. PDOS spectra highlight changes in electronic structure between related complexes. Trends in oxidation potential are reproduced by the position of the metal PDOS peak. Predicted Raman frequencies agree well with experiment, although a scaling factor is required. Adsorption of an osmium complex on a gold surface causes molecular orbitals close to the surface to shift, while the relative positions of other molecular orbitals remain unchanged. The oxidised complex binds more strongly, due to the change in the nature of the frontier orbitals.