This thesis is devoted to modelling the effects of surface roughness, on performance, in lubricated contact interfaces found inside and between various machine elements. Many researchers have of course already addressed this, both experimentally and numerically, however, due to the multidisciplinary nature and the complexity of the associated theoretical models, the progress in the development of efficient yet user friendly software has not reached as far as in other fields. Especially the requirement on mesh density to resolve the surface roughness is difficult to meet and it is through this connection that this thesis contributes to the field of research. Namely, by development and implementation of rigorous theoretical models that allow for effective numerical treatment of this type of problems. This thesis work has, through a remarkably successful collaboration with a research group in mathematics specialized in homogenization, also led to advances in applied mathematics and the outcome of this work spans the whole range from new theorems in applied mathematics to contract research, considering modern industrial applications.