This report was originally written to fulfill in part the requirements of the author's WPE examinations, part of the qualifying examinations for the University of Pennsylvania'a Computer Science Ph.D program. The report first introduces CCS and uses it to illustrate various features of established methods of modelling concurrent, communicating systems. The report then goes on to describe and investigate two new models for such systems: The Chemical Abstract Machine, a simple yet predominant in most models for such systems; and the π-calculus, a calculus similar in many respects to CCS, but able to model mobile processes and other, more difficult phenomena.