The development of innovative technologies based on employing green energy carriers, such as hydrogen, is becoming high in demand, especially in the automotive sector, as a result of the challenges associated with sustainable mobility. In the present review, a detailed overview of the entire hydrogen supply chain is proposed, spanning from its production to storage and final use in cars. Notably, the main focus is on Polymer Electrolyte Membrane Fuel Cells (PEMFC) as the fuel-cell type most typically used in fuel cell electric vehicles. The analysis also includes a cost assessment of the various systems involved; specifically, the materials commonly employed to manufacture fuel cells, stacks, and hydrogen storage systems are considered, emphasizing the strengths and weaknesses of the selected strategies, together with assessing the solutions to current problems. Moreover, as a sought-after parallelism, a comparison is also proposed and discussed between traditional diesel or gasoline cars, battery-powered electric cars, and fuel cell electric cars, thus highlighting the advantages and main drawbacks of the propulsion systems currently available on the market.