Engines and other machines with moving parts are often limited in their design and operational lifetime by friction and wear. This limitation has motivated the study of fundamental tribological processes with the ultimate aim of controlling and minimizing their impact. The recent development of miniature apparatus, such as microelectromechanical system (MEMS) microelectromechanical systems (MEMSmicroelectromechanical system (MEMS)nanometer-scaledeviceatomic frictions) and nanometer-scale devices, has increased interest in atomic-scale friction, which has been found to, in some cases, be due to mechanisms that are distinct from the mechanisms that dominate in macroscale friction. Presented in this chapter is a review of computational studies of tribological processes at the atomic and nanometer nanometer scale. In particular, a review of the findings of computational studies of nanometer-scaleindentation nanometer-scale indentation, nanometer-scalefriction friction and lubrication nanometer-scalelubrication is presented, along with a review of the salient computational methods that are used in these studies, and the conditions under which they are best applied.