In this work, reverse osmosis water desalination plants powered by PV and solar RC cycle systems are reviewed in detail. This review focused on the display of different designs and software used to improve productivity of the desalination plants as well as the types of solar collectors used, membrane, heat transfer fluid and working fluid of the Rankine cycle. The specific energy consumption and cost of fresh water production are also of great interest in this work. According to the results presented in this review it is not recommended to use batteries with PV to drive RO desalination plants because of the high capital and replacement cost of batteries. It is also found that when the energy recovery devices are used, the pre-heating of feed water is not required, especially in the case of PV-RO systems. Currently most of working RO plants are driven by PV, whereas solar thermal power systems (usually using PTC with ORC) are still at the stage of theoretical research. Although, the PTC-ORC-RO desalination system is recommended, it has not yet been implemented on a large scale.