The theoretical examination of the friction between solids is discussed with a focus on self-assembled monolayers, carbon-containing materials and antiwear additives. Important findings are illustrated by describing examples where simulations have complemented experimental work by providing a deeper understanding of the molecular origins of friction. Most of the work discussed herein makes use of classical molecular dynamics (MD) simulations. Of course, classical MD is not the only theoretical tool available to study friction. In view of that, a brief review of the early models of friction is also given. It should be noted that some topics related to the friction between solids, i.e. theory of electronic friction, are not discussed here but will be discussed in a subsequent review.