A major challenge for the maritime industry during the last decades lies with its “obligation” to reduce the greenhouse gas (GHG) emissions from its operations and contribute to both global and regional targets for climate neutrality and decarbonization, like the Paris Agreement and the European Green Deal. In this direction, the “IMO Initial Strategy for the Reduction of GHG emissions from Shipping” calls for urgent action in order to reduce shipping GHG emissions by 50% by 2050 -when compared to 2008- and completely decarbonize the industry before the end of this century. The replacement of fossil fuels by alternative fuels and energy sources is absolutely necessary in this respect and a number of alternative fuels with GHG emission reduction potential have been proposed and considered for marine application. Among the different marine fuels, hydrogen and ammonia seem to have the higher environmental benefits and potential to achieve the decarbonization of maritime transport, but their adoption comes with high capital investments for the installation of new engines and fuel systems, port infrastructure, and increased operational costs due to their high prices compared with the conventional fuels. This paper analyses the costs and benefits associated with the use of hydrogen and ammonia as marine fuels focusing on various production methods, comprising blue fuels – produced from fossil sources and using carbon and capture storage (CCS) - and green fuels – coming from renewable energy sources. A cost-benefit analysis of the use of hydrogen and ammonia as marine fuels is essential in order to specify and underline the cost differences between these fuels and the conventional ones and make policy recommendations on how this existing ‘cost gap’ could be somehow alleviated through market-based measures (MBMs) to stimulate further investments on these fuels. Additional identified challenges associated with the use of these fuels – including availability, safety and regulatory aspects - are also touched upon in this paper.