The objective of this dissertation is to enhance the overall understanding of practical manufacturing systems by using rigorous academic approaches, primarily queueing theory. The scope spans from the performance of a single manufacturing process to the performance of a manufacturing system. Queueing models are commonly used to evaluate the performance of manufacturing systems. Exact M/M/1 or approximations of G/G/1 models are usually adopted to describe the behavior of a single machine system. However, when applying queueing models to a single machine, some practical issues are encountered. A real machine is subject to different types of interruptions, such as breakdowns, setups and routine maintenance. The proper queueing models under interruptions are presented. The behavior of manufacturing systems is explored by first investigating the underlying structure of tandem queues. We introduce two properties describing the dependence among servers in tandem queues, namely the intrinsic gap and intrinsic ratio, and develop a new approximation approach. The approach exploits what we call the nearly-linear and heavy-traffic properties of the intrinsic ratio. Across a broad range of examined cases, this new approach outperforms earlier approximations that are based on the parametric-decomposition and diffusion approximation approaches. We also demonstrate its use with historical data to achieve very accurate queue time estimates. Furthermore, based on the structure of tandem queues, a way to model the performance of manufacturing systems has been developed.