The maritime industry is undergoing a technology transition that aims to increase the use of low-emission fuels. There is a significant trend visible of new ships being ordered with alternative fuel propulsion. In the future shipping’s fuel market will be more diverse and it will rely on multiple energy sources. One of the very promising ways to meet the International Maritime Organisation’s decarbonization requirements is to operate ships with sustainable hydrogen propulsion. One of the possible options to limit greenhouse gases emissions is the production of low-carbon ‘green’ hydrogen by water electrolysis using low-carbon electricity. This hydrogen can then be used directly in fuel cells to produce electricity or in the internal combustion engines, without having a carbon impact and pollutant emissions. Hydrogen can also be converted into its derivatives. This paper presents a review of recent studies of ships’ hydrogen propulsion systems, different aspects of production, transportation, storage, and using liquid/gaseous H2 and its derivatives as a fuel in the shipping industry. H2 propulsion in maritime transport is still in the experimental phase. In most cases, these experiments serve as a kind of platform for evaluating the applicability of different technological solutions. This article presents existing ships’ hydrogen and its derivates propulsion systems, projects, and existing conceptual studies.