One of the most effective ways to minimize supply/demand mismatch cost, with little increase in operational cost, is to deploy valuable resources in a flexible and timely manner to meet the realized demand. This notion of flexible processes has significantly changed the operations in many manufacturing and service companies. For example, flexible production system is now commonly used by automobile manufacturers, and work force cross-training system is by now a common practice in many service industries. However, there is a tradeoff between the level of flexibility available in the system and the associated complexity and operational cost. The challenge is to have the "right" level of flexibility to capture the bulk of the benefits from a full flexibility system, while controlling for the increase in implementation cost. This paper reviews the latest development on the subject of process flexibility in the past decade. In particular, we focus on the phenomenon, often observed in practice, that a slight increase in process flexibility can reap a significant amount of improvement in system performance. This review explores the issues in three perspectives: design, evaluation and applications. We also discuss how the process flexibility concept has been deployed in several manufacturing and service systems.