Advances in experimental techniques over the last decade have resulted in the realisation ofatomically precise doping of silicon and the creation of single dopant devices. Therefore, a greater theoretical understanding of deep dopant structures and the resulting defect complexes are required. In this thesis, we apply a variety of computational methods based on density functional theory (DFT) to the study of dopants and defect centres in bulk silicon and silicon nanostructures. The calculations are performed using the plane wave based code VASP and the linear scaling code CONQUEST. Firstly, we discuss the effects of self-compensation in p-type doped bulk silicon in the casestudy of single aluminium dopants and aluminium dopant pairs in bulk silicon. We consider the formation of dimer type complexes and determine whether such complexes will be electrically active. We then investigate the formation of dopant vacancy pairings in silicon using bismuth dopants, which are not commonly used in the semiconductor industry but may be used tofabricate solotronic devices or for quantum information processing type applications. TheDFT simulations performed are compared with experimental data. The incorporation of phosphorus in silicon is also studied within this by analysing phosphorus delta-doped layers. The effects of dopant depth and the diffusion of delta-doped layers upon the electronic structure are presented. Furthermore, this thesis includes some developmental work attempting to improve upon the efficiency multi-site support functions when used in conjunction with the linear scaling methods within the Conquest code.