We discuss recent advances in developing a fundamental, mechanistic, understanding of the evolution of surface roughness of solids during dry sliding. The time evolution of surface roughness is little understood although it crucially impacts friction and wear. Engineering wear models are for the most part empirical, and the development of physics-based predictive models will require intensive experimental, theoretical and numerical research at various scales. This presentation focuses on atomistic and mesoscale numerical modelling of rough solids under sliding in the presence of adhesive wear mechanisms.