In this chapter we give a brief overview of the significant technological changes which have occurred since the 1950s. The importance of information technology in manufacturing systems and the need for the designer to have performance measures other than throughput in mind during the design process is treated. A presentation of some areas in mathematical analysis, which are important for our work, is contained in Appendix A. In Section 1.1, the evolution and classification of manufacturing systems is covered. Section 1.2 treats mathematical models and the modeling process. Section 1.3 attempts a general classification of manufacturing systems with a view to showing the inherent complexities. Section 1.4 discusses models in the context of manufacturing systems, whereas Section 1.5 treats methods of analysis of such models. Finally, Section 1.6 presents measures of performance in manufacturing systems.