Solar desalination systems are approaching technical and cost viability for producing fresh-water, a commodity of equal importance to energy in many arid and coastal regions worldwide. Solar photovoltaics (PV) represent an ideal, clean alternative to fossil fuels, especially for remote communities such as grid-limited villages or isolated islands. These applications for water production in remote areas are the first to be nearing cost-competitiveness due to decreasing PV prices and increasing fossil fuel prices over the last five years. The electricity produced from PV systems for desalination applications can be used for electro-mechanical devices such as pumps or in direct-current (DC) devices. Reverse osmosis (RO) and electrodialysis (ED) desalination units are the most favorable alternatives to be coupled with PV systems. RO usually operates on alternating current (AC) for the pumps, thus requiring a DC/AC inverter. In contrast, electrodialysis uses DC for the electrodes at the cell stack, and hence, it can use the energy supplied from the PV panels with some minor power conditioning. Energy storage is critical and batteries are required for sustained operation. In this paper, we discuss the operational features and system designs of typical PV-RO and PV-ED systems in terms of their suitability and optimization for PV operation. For PV-RO and PV-ED systems, we evaluate their electricity need, capital and operational costs, and fresh-water production costs. We cover ongoing and projected research and development activities, with estimates of their potential economics. We discuss the feasibility of future solar desalination based on expected (or predicted) improvements in technology of the desalination and PV systems. Examples are provided for Middle East and other parts of the World.