Due to the increasing impact of ship emissions on the environment and the preventive measures of current regulations introduced by the International Maritime Organization to significantly reduce them, the development of ocean-going all-electric ships has been addressed as a concept applied to achieve it. Being a promising technology considers the use of technology alternatives such as fuel cells, batteries, and supercapacitors together with the use of zero-carbon alternative fuels such as hydrogen (H2) and ammonia (NH3) as main energy sources. This article addresses a state-of-the-art on several challenges related to the ocean-going zero-emissions ship to achieve a zero-emissions shipping, based on the technology associated with hybrid and all-electric ship, and the zero-carbon fuels alternatives. In this respect, a transition from fossil fuel-based propulsion and auxiliary systems to a zero-emissions ship concept are related to the challenges to overcome the needs of energy density for these new alternatives energy sources compared to current fossil fuel options. The transitional process should consider a first step of hybridization of the propulsion and auxiliary systems of existing ships to get a baseline from where to move forward to a zero-emissions configuration for new designs.