This review brings out those aspects of the development of proton exchange membrane (PEM) fuel cells over the last two to three decades that are of interest to the heat and mass transfer community. Because the heat transport and mass transport in proton exchange membrane fuel cells are very important from the efficiency point of view, an emphasis is given here to these transports and their influence on operating cell parameters. The works are classified as models with either isothermal or non-isothermal conditions of various assumed dimensionality and with either single-phase or two-phase flow. Along with modeling, a few experimental studies available are also reported here. Researchers in the area of PEM fuel cells are involved in activities such as development of new and low-cost materials, modeling the relevant physical processes, and electrochemical experimentation. These collective efforts may lead to making this technology viable to meet world needs for clean and cheap energy. This review brings out the fact that computational fluid dynamics (CFD) has become an inevitable tool in fuel cell analysis, as the detailed interactions between the flow structure geometry, fluid dynamics, multiphase flow, heat transfer, mass transfer, and electrochemical reaction can be modeled simultaneously, given the present state of the art in CFD. Through the predictive capability of CFD, it will be possible for fuel cell designers to better optimize the design and operating parameters of fuel cells before testing them in laboratory.