Soilless growing has been practiced since ancient times. Ancient Babylonians, Egyptians and Aztecs were known to grow plants hydroponically.
The chemical nutrients to be dissolved in the water can be derived entirely synthetically, or entirely organically, or some combination of both. Modern industrial growing systems usually include dosing machines which measure the nutrient level and pH in the solution, and add nutrients or pH balancers as required.
The roots of the plants are supported in some form of inert or semi-inert medium. One of the oldest media is simple sand, which was inexpensive and easy to obtain. Scoria (a volcanic rock) and expanded clay balls have also been used, but their excessive weight is a disadvantage. There are other mineral-based media which are more advantage, having been heat treated to modify the physical structure. Perlite and vermiculite are manufactured by the high temperature treatment and expansion of aluminium silicate and mica respectively. Horticultural rockwool is manufactured by heating a mixture of basalt, limestone and silica to 1600 degrees celsius and then spinning the molten slag into fibres. Other popular media, particularly in less developed locations, are coir (coconut husk) and peanut hulls. All of these media function to support the root structures of the plans while allowing them to contact the nutrient solution.
The simplest hydroponic systems do not recycle the nutrient solution, but instead allow it to run off. These are not very efficient, but are suitable for domestic gardening. The nutrient solution can act as a true "complete fertiliser" when allowed to run to a lawn or garden.
Commercial systems recycle the nutrient solution to maximise efficient use of water and nutirent. The three most common systems used in commercial growing are Nutrient Film Technique (usually simply called NFT), "flood and drain", and drip feed. NFT involves running a constant stream of nutrient solution over the plant roots in a thin film. The flow rates are fairly high, and oxygenation of the roots is favourable, but this solution is very sensitive to system failure. A pump stoppage of a few minutes could result in the roots drying out and the plants dying. Flood and drain, sometimes called table drain, systems alternatively flood the medium with nutrient solution and allow the solution to drain away. As long as the time between drainning and re-flooding is managed, the plants roots will not dry out. If a pump fails, the drain can be plugged while repairs are underway. Drip feed, as the name suggests involves the dripping of the nutrient solution directly onto the plant roots. 
Hydroponics covers an extremely wide technological range. Some commercial growers use the most advanced computer controlled environments micro-managing the entire environment of the plants, including the water, nutrient, atmospheric gases, temperature, winds, light levels and spectra. In contrast, aid organisations sometimes provide disaster survivors in under developed locations with “self sufficiency” systems consisting of a flood & drain table with coir medium, seeds or seedlings, and a bucket for liquid manure.