In principle, the propulsion technologies available to ships are not that different to the ones available for other types of vehicles. The difference is that the ship’s propulsion system is powering a single-screw (or sometimes twin-screw) planted propeller to create the necessary thrust to move the ship .
The most common propulsion system in ships is currently still the diesel combustion engine to power the ship’s screw. Often, this type of engine is controlled electrically instead of mechanically like it used to be in the past . These combustion engines can rely on a variety of different fuel types: While carbon-based fuel types that are the result of different refinement steps of crude oil, like heavy fuel oil (HFO), marine gas oil (MGO) or marine diesel oil (MDO). And while there are also bio fuels (bio-diesel) available, they are not suitable for commercial use yet except when being mixed with mineral fuel . A more promising and environmentally friendlier alternative to traditional fuels is liquified natural gas (LNG) which not only significantly “reduc[es] pollutant and greenhouse gas emissions”  but also only requires conventional combustion engines to be retrofitted to dual-fuel engines to run on LNG. 
Additionally, LNG requires storage in a cryogenic tank to maintain its liquid form.  A survey by Maritime Research Partners underlines the importance of LNG as fuel of the future: 71,1 % of respondents mentioned the usage of LNG as a means to reduce emissions in the shipping industry. 
Also, electric motors and diesel-electric hybrids are on the rise as propulsion systems for ships and are especially relevant for small vessels that travel short distances at a time. In Norway for example, there are already fully electrified ferries in use. 
This trend is supported by the fact that of all ordered car and passenger ferries with alternative propulsion systems in 2019, approximately 75% had either electric or hybrid engine technologies. 
Of course there are many other technologies available to be used in shipping vessels: Solar power, wind energy and synthetic fuels are just some of the ones that currently are too much of niche technologies to focus on here. 
 MAN Energy Solutions. (2018). Basic principles of ship propulsion. https://www.man-es.com/docs/default-source/marine/tools/basic-principles-of-ship-propulsion_web_links.pdf?sfvrsn=12d1b862_10. pp.15f.
 MAN Energy Solutions. (2018). Basic principles of ship propulsion. https://www.man-es.com/docs/default-source/marine/tools/basic-principles-of-ship-propulsion_web_links.pdf?sfvrsn=12d1b862_10. pp.29f.
 ShipInsight. (2019, July 11). Explaining the types of fuel used on ships. https://shipinsight.com/articles/explaining-the-types-of-fuel-used-on-ships/.
   Deutsches Zentrum für Luft- und Raumfahrt e.V. (DLR). (2011, December 19). LNG as an alternative fuel for the operation of ships and heavy-duty vehicles: Short study in the context of the scientific supervision, support and guidance of the BMVI in the sectors Transport and Mobility with a specific focus on fuels and propulsion technologies, as well as energy and climate. pp.10-32.
   Statista. (2021, November 17). Statista-Dossier: Trends im Schiffbau. https://de.statista.com/statistik/studie/id/85394/dokument/trends-im-schiffbau/. pp.27-40.
 Leigh, G. (2021, July 3). Travel Norway's Fjords on a Quiet Electric Ferry. https://www.bloomberg.com/news/articles/2021-07-03/travel-norway-s-fjords-on-a-quiet-electric-ferry.