Proton exchange membrane (PEM) electrolysis is widely considered an integral part of the energy transition. Thinner membranes can reduce Ohmic losses and increase efficiency. However, hydrogen crossover limits the use of thinner membranes. For the first time, this review provides a comprehensive overview of both model and experimental works on hydrogen crossover and crossover mitigation. By combining the experimental data and state-of-the-art models, we discuss the recent progress in understanding crossover mechanisms. The dominant mechanism for hydrogen crossover is the diffusion driven by both the high hydrogen partial pressures at the cathode and supersaturation in the catalyst layer due to transport limitations. The reviewed models successfully reproduce the experimental data obtained by different groups. A variety of strategies for including recombination catalysts in the cell are currently investigated in academic and corporate research. Some of these show promising results with potential for near-term industrial application.