Desalination plants, which provide drinking water for residents, rely on electricity generated by fossil fuels. However, the excessive use of fossil fuels leads to their rapid depletion and has detrimental effects on the environment. Thus, the use of renewable energy resources in water desalination has gained popularity. The current research investigates the integration of renewable energy systems with seawater and brackish water desalination technologies. In this regard, three primary renewable energy sources—wind, solar, and geothermal—are selected. Accordingly, a thorough investigation of the related research published and the trend of evolutions between 2013 and 2023 is carried out for Reverse Osmosis (RO), Multistage flash (MSF), and Multi-effect distillation (MED)-based water desalination facilities coupled with renewable energy sources. In our investigation, we particularly focus on performance indicators, energy efficiency, economic factors, and environmental effects. Also, the associated challenges of these hybrid systems, such as technological complexity, unpredictability, and intermittency, are addressed. Prospects for the future that address these issues and the prospects of using renewable energy in water desalination technologies are also covered.