This review summarizes recent advances in the application of 3D printing (additive manufacturing) for the fabrication of various components of hydrogen fuel cells with a polymer electrolyte membrane (HFC-PEMs). This type of fuel cell is an example of green renewable energy, but its active implementation into the real industry is fraught with a number of problems, including rapid degradation and low efficiency. The application of 3D printing is promising for improvement in HFC-PEM performance due to the possibility of creating complex geometric shapes, the exact location of components on the substrate, as well as the low-cost and simplicity of the process. This review examines the use of various 3D printing techniques, such as inkjet printing, fused deposition modeling (FDM) and stereolithography, for the production/modification of electrodes, gas diffusion and catalyst layers, as well as bipolar plates. In conclusion, the challenges and possible solutions of the identified drawbacks for further development in this field of research are discussed. It is expected that this review article will benefit both representatives of applied science interested in specific engineering solutions and fundamental science aimed at studying the processes occurring in the fuel cell.