Marine sources contribute approximately 2% of global energy-related CO₂ emissions, with the shipping industry accounting for 87% of this total, making it the fifth-largest emitter globally. Environmental regulations by the International Maritime Organization (IMO), such as the MARPOL (International Convention for the Prevention of Pollution from Ships) treaty, have driven the exploration of alternative green energy solutions, including nuclear-powered ships. These ships offer advantages like long operational periods without refueling and increased cargo space, with around 200 reactors already in use on naval vessels worldwide. Among advanced reactor concepts, the molten salt reactor (MSR) is particularly suited for marine applications due to its inherent safety features, compact design, high energy density, and potential to mitigate nuclear waste and proliferation concerns. However, MSR systems face significant challenges, including tritium production, corrosion issues, and complex behavior of volatile fission products. Understanding the impact of marine-induced motion on the thermal–hydraulic behavior of MSRs is crucial, as it can lead to transient design basis accident scenarios. Furthermore, the adoption of MSR technology in the shipping industry requires overcoming regulatory hurdles and achieving global consensus on safety and environmental standards. This review assesses the current progress, challenges, and technological readiness of MSRs for marine applications, highlighting future research directions. The overall technology readiness level (TRL) of MSRs is currently at 3. Achieving TRL 6 is essential for progress, with individual components needing TRLs of 4–8 for a demonstration reactor. Community Readiness Levels (CRLs) must also be addressed, focusing on public acceptance, safety, sustainability, and alignment with decarbonization goals.