Hydrogen as an energy carrier could help decarbonize industrial, building, and transportation sectors, and be used in fuel cells to generate electricity, power, or heat. One of the numerous ways to solve the climate crisis is to make the vehicles on our roads as clean as possible. Fuel cell electric vehicles (FCEVs) have demonstrated a high potential in storing and converting chemical energy into electricity with zero carbon dioxide emissions. This review paper comprehensively assesses hydrogen’s potential as an innovative alternative for reducing greenhouse gas (GHG) emissions in transportation, particularly for on-board applications. To evaluate the industry’s current status and future challenges, the work analyses the technology behind FCEVs and hydrogen storage approaches for on-board applications, followed by a market review. It has been found that, to achieve long-range autonomy (over 500 km), FCEVs must be capable of storing 5–10 kg of hydrogen in compressed vessels at 700 bar, with Type IV vessels being the primary option in use. Carbon fiber is the most expensive component in vessel manufacturing, contributing to over 50% of the total cost. However, the cost of FCEV storage systems has considerably decreased, with current estimates around 15.7 $/kWh, and is predicted to drop to 8 $/kWh by 2030. In 2021, Toyota, Hyundai, Mercedes-Benz, and Honda were the major car brands offering FCEV technology globally. Although physical and chemical storage technologies are expected to be valuable to the hydrogen economy, compressed hydrogen storage remains the most advanced technology for on-board applications.