The maritime sector has thrived on using fossil hydrocarbon fuels, such as heavy fuel oil (HFO) and marine diesel oil (MDO). These fuels allowed vessels to carry large amounts of cargo over large distances, due to their high energy density. However, the climate objectives of the Paris agreement and the ever-tightening legislation regarding harmful emissions, such as nitrogen oxides (NOX), sulphur oxides (SOX) and particulate matter (PM) require the phasing out of fossil fuels. The production of a renewable replacement for diesel is costly and requires a source of carbon. Therefore, renewable alternatives are most likely less energy dense than the diesel that is currently used. The transition to non-fossil energy carriers will thus be challenging for vessels that have a high power density, require a large autonomy, operate globally and/or have a challenging fuel logistics. This paper presents a pathway to a carbon neutral maritime sector with nearly no harmful emissions. This transition calls for the development and implementation of clean and efficient energy conversion technologies on board vessels. In addition, efficient and cost effective production of alternative fuels is required, as well as the development of an adequate bunker infrastructure. Government policies to subsidise clean solutions and, if needed, tax emissions, need to be put in place to support these developments. These actions are preferably taken sooner rather than later, since vessels have a relatively long service life and, subsequently, a slow replacement rate. Alternative energy carriers and drive system technologies are assessed based on their technology readiness and environmental impact. Each alternative is judged based on the total costs of ownership, as there is a trade-off between the technical developments, emission legislation, investment and the operational costs. The effect of government policy on the viability of the alternatives is also demonstrated.