Interest in diffusion processes in SiGe alloys arises from their potential in HBT's, HFET's, and optoelectronics devices, where migration over distances as small as a few nanometres can be significant. Successful modelling of these processes requires a much improved understanding of the mechanisms of self- and dopant diffusion in the alloy, although recent progress has been made. It is the purpose of this review to set this in the context of diffusion processes in elemental silicon and germanium, and to identify how this can help to elucidate behaviour in the alloy. Firstly, self diffusion processes are reviewed, from general agreement that self-diffusion in germanium is dominated by neutral and acceptor vacancies, to the position in silicon which is still uncertain. Germanium diffusion in silicon, however, appears to be via both vacancy and interstitial processes, and in the bulk alloy there is evidence for a change in dominant mechanism at around 35 percent germanium. Next, a review of dopant diffusion begins with Sb, which appears to diffuse in germanium by a mechanism similar to self-diffusion, and in silicon via monovacancies also, from marker layer evidence. In SiGe, the effects of composition and strain in epitaxial layers on Si substrates are also consistent with diffusion via vacancies, but questions still remain on the role of charged defects. The use of Sb to monitor vacancy effects such as grown-in defects by low temperature MBE, are discussed. Lastly, progress in assessing the role of vacancies and interstitials in the diffusion of boron is reviewed, which is dominated by interstitials in silicon-rich alloys, but appears to change to domination by vacancies at around 40 percent germanium, although studies in pure germanium are greatly needed.