The marine industry must reduce emissions to comply with recent and future regulations. Solid oxide fuel cells (SOFCs) are seen as a promising option for efficient power generation on ships with reduced emissions. However, it is unclear how the devices can be integrated and how this affects the operation of the ship economically and environmentally. This paper reviews studies that consider SOFC for marine applications. First, this article discusses noteworthy developments in SOFC systems, including power plant options and fuel possibilities. Next, it presents the design drivers for a marine power plant and explores how an SOFC system performs. Hereafter, the possibilities for integrating the SOFC system with the ship are examined, also considering economic and environmental impact. The review shows unexplored potential to successfully integrate SOFC with thermal and electrical systems in marine vessels. Additionally, it is identified that there are still possibilities to improve marine SOFC systems, for which a holistic approach is needed for design at cell, stack, module, and system level. Nevertheless, it is expected that hybridisation is needed for a technically and economically feasible ship. Despite its high cost, SOFC systems could significantly reduce GHG, NOX, SOX, PM, and noise emissions in shipping.