Friction between two solid bodies in relative sliding motion takes place on a large spectrum of length and time scales: From the nanometer/second scale in an atomic force microscope up to the extremely macroscopic scales of tectonic motion. Despite our familiarity with the effects of friction, fundamental questions remain unanswered. The atomistic origins of well-established phenomenological friction laws are controversial. Many explanations, seemingly well-established, have recently been called into question by new experimental results. Computer simulations have also revealed flaws in previous theoretical approaches and led to new insights into the atomistic processes responsible for friction. In this chapter, selected computer simulation studies of friction and their implications will be discussed. Emphasis will be given to the question what one can learn from a friction simulation and how it is possible to avoid effects that merely arise due to poor models. Moreover, it will be outlined how it is possible to gain insight into tribological processes that take place on macroscopic time scales with the help of atomistic computer simulations, which are typically constrained to the nanosecond regime.