Flow field designs for the bipolar plates of the proton exchange membrane fuel cell are reviewed; including the serpentine, parallel, interdigitated, mesh type or their mixtures, furthermore 2D circular and 3D tubular geometries, porous, fractal, and biomimetic flow fields. The advantages/disadvantages and tendencies from field optimizations are discussed. The performance of each flow field design is compared to the conventional serpentine flow field. Good flow field plates give uniform gas distributions, low pressure drop for transport, and sufficient rib area to provide high electronic conductivity. A good field should also prevent water condensation, remove water efficiently, and provide sufficiently high moisture content in the membrane. The demands on design are sometimes contradictory. Future work should aim for a flow field geometry and topology that produces uniform gas delivery at a low pressure-drop, and at the same time has an optimal channel shape for better water removal. It is concluded that for an area-filling gas distributor, the developments should aim to find a flow field in accordance with minimum entropy production, making an emphasis on multi-criteria optimization methods.