Simultaneous heat and mass exchange devices such as cooling towers, humidifiers and dehumidifiers are widely used in the power generation, desalination, air conditioning, and refrigeration industries. For design and rating of these components it is useful to define their performance by an effectiveness. In this paper, several different effectiveness definitions that have been used in literature are critically reviewed and an energy based effectiveness which can be applied to all types of heat and mass exchangers is defined. The validity and the limitations of the various effectiveness definitions are demonstrated by way of several examples including direct and indirect contact, parallel and counterflow heat and mass exchangers. The limiting case of a simple heat exchanger is also discussed. The importance of thermal balancing in minimizing entropy production and its implications for optimization and design of these devices is dealt with in detail. The application of the energy effectiveness to heat-exchanger-like ε-NTU correlations is also examined using a detailed numerical model.