To reduce pollution from ships in coastal and international navigation, shipping companies are turning to various technological solutions, mostly based on electrification and the use of alternative fuels with a lower carbon footprint. One of the alternatives to traditional diesel fuel is the use of hydrogen as a fuel or hydrogen fuel cells as a power source. Their application on ships is still in the experimental phase and is limited to smaller ships, which serve as a kind of platform for evaluating the applicability of different technological solutions. However, the use of hydrogen on a large scale as a primary energy source on coastal and ocean-going vessels also requires an infrastructure for the production and safe storage of hydrogen. This paper provides an overview of color-based hydrogen classification as one of the main methods for describing hydrogen types based on currently available production technologies, as well as the principles and safety aspects of hydrogen storage. The advantages and disadvantages of the production technologies with respect to their application in the maritime sector are discussed. Problems and obstacles that must be overcome for the successful use of hydrogen as a fuel on ships are also identified. The issues presented can be used to determine long-term indicators of the global warming potential of using hydrogen as a fuel in the shipping industry and to select an appropriate cost-effective and environmentally sustainable production and storage method in light of the technological capabilities and resources of a particular area.