Much of the complexity in modern enterprises emerges from the nonlinear and likely chaotic dynamics of the underlying processes. These processes are defined over multiple scales of system granularity, for e.g., supply chain-level, through shop floors, down to a machine or a core physical operation level. Characterization of this complexity is imperative for improving predictability of quality and performance in modern physical and engineered systems. In this paper we present some theoretical developments and tools aimed at advancing the applications of nonlinear dynamic systems principles in manufacturing processes and systems, with specific emphasis on characterizing and harnessing chaos in these complex systems.We examine the current developments in addressing predictability in two important facets of a manufacturing enterprise, namely, process level characterization and monitoring, and systems level characterization. For each case, we concisely evaluate the relevant alternative approaches and layout certain open issues. We hope that this paper will spur further development of methodologies adapting nonlinear dynamics and chaos principles for advancing various aspects of manufacturing enterprises.