Heat transfer optimization methods to effectively improve heat transfer performance is of great importance for energy conservation and pollution reduction. A recently developed heat transfer optimization method based on entransy theory and related peer-reviewed papers published between 2003 and 2010 are reviewed and updated in this paper to describe entransy, entransy dissipation, optimization criteria and optimization principles and their applications to different heat transfer modes (thermal conduction, convection and radiation) and to different levels (heat transfer element, heat exchanger, and heat exchanger network). Entransy theory is then compared with entropy theory in several aspects, including the heat transfer purpose, irreversibility and optimization principle for energy savings or weight reductions of thermal facilities. Finally, entransy theory is also compared with constructal theory in terms of optimization objective, optimization method and optimized results. (c) 2013 Elsevier Ltd. All rights reserved.