Desalination has become imperative as a drinking water source for many parts of the world. Due to the large quantities of thermal energy and high quality electricity requirements for water purification, the desalination industry depends on waste heat resources and renewable energy sources such as solar collectors, photovoltaic arrays, geothermal and wind and tidal energy sources. Considering the mismatch between the source supply and demand and intermittent nature of these energy resources, energy storage is a must for reliable and continuous operation of desalination facilities. Thermal energy storage (TES) requires a suitable medium for storage and circulation while the photovoltaic/wind generated electricity needs to be stored in batteries for later use. Desalination technologies that utilize thermal energy and thus require storage for uninterrupted process operation are multi-stage flash distillation (MSF), multi-effect evaporation (MED), low temperature desalination (LTD) and humidification–dehumidification (HD) and membrane distillation (MD). Energy accumulation, storage and supply are the key components of energy storage concept which improve process performance along with better resource economics, and minimum environmental impact. Similarly, the battery energy storage (BES) is essential to store electrical energy for electrodialysis (ED), reverse osmosis (RO) and mechanical vapor compression (MVC) technologies. This research-review paper provides a critical review on current energy storage options for different desalination processes powered by various renewable energy and waste heat sources with focus on thermal energy storage and battery energy storage systems. Principles of energy storage (thermal and electrical energy) are discussed with details on the design, sizing, and economics for desalination process applications.