The “standard heat exchanger network problem” has been surprisingly difficult to solve. It is only now that simple and reliable methods have evolved to synthesize the most efficient network of heat exchangers to heat and cool known process streams between stated temperature bounds. This has taken over a decade of research and scores of publications. The “resilient heat exchanger network problem” requires a solution that can cope with the uncertainties of industrial design. Fixed flow rates and temperature bounds rarely occur industrially. Rather, an industrial heat exchanger network problem necessarily involves ranges of flow rates and ranges of temperature bounds, and must include ease of operation and control. In this paper we make several fundamental advances in the design of resilient heat exchanger networks. (1) An efficient design procedure is developed to yield resilient designs which handle fluctuations within the condition of maximum energy efficiency. (2) A control structure and operating policy are developed to adjust flow distributions in the network to meet temperature constraints with minimum utility usage. These developments are based on several new theorems concerning resiliency in network design.