Carbon capture on-board ships represents a powerful technological measure in order for the shipping industry to meet the very stringent GHG emission reduction requirements. Operation within the ship environment introduces a number of constraints associated mainly with space, energy supply, and safety which have to be addressed using compact yet efficient solutions. To this end, solvent-based membrane CO2 capture offers several advantages and has the necessary technological maturity for on-board installation. Solvent choice remains a critical issue both for reasons associated with process efficiency as well as on-board safety. In this paper, we present an up-to-date comprehensive review of the different solvents that can be used for post-combustion CO2 capture. Furthermore, we investigated the solvents’ performance as determined by their inherent characteristics, properties, and behavior for a range of operating conditions against the strict shipping requirements. A preliminary qualitative comparative assessment was carried out based on appropriately selected key performance indicators (KPIs) pertinent to the requirements of the shipping industry. The identified solvent classes were compared using the most critical KPIs for system integration with the ship. It was concluded that at present, no solvent category can efficiently address all the requirements of the ship. However, widely used solvents such as secondary amines showed relatively good compatibility with the majority of the introduced KPIs. On the other hand, more recently developed molecules, such as phase change solvents and ionic liquids, can easily prevail over the vast majority of the identified solvents as long as they are brought to the same level of technological maturity with benchmark solvents. Such a conclusion points toward the need for accelerating research on more tailor-made and performance-targeted solvents.