The present review provides an overview of the basic theory of sputtering with recent models, focussing in particular on sputtered atom energy distribution functions. Molecular models such as Monte-Carlo, kinetic Monte-Carlo, and classical Molecular Dynamics simulations are presented due to their ability to describe the various processes involved in sputter deposition at the atomic and molecular scale as required. The sputter plasma, the sputtering mechanisms, the transport of sputtered material and its deposition leading to thin film growth can be addressed using these molecular simulations. In all cases, the underlying methodologies and some selected mechanisms are highlighted.