Natural oil polyols
Natural oil polyols, also known as NOPs, are polyols derived from vegetable oils by several different techniques. The primary use for these materials is in the production of polyurethanes. Most NOPs qualify as Biobased Products, as defined by the United States Secretary of Agriculture in the Farm Security and Rural Investment Act of 2002.
NOPs all have similar sources and applications, but the materials themselves can be quite different, depending on how they are made. All are clear liquids, ranging from colorless to medium yellow. Their viscosity is also variable and is usually a function of the molecular weight and the average number of hydroxyl groups per molecule (higher mw and higher hydroxyl content both giving higher viscosity.) Odor is a significant property which is different from NOP to NOP. Most NOPs are still quite similar chemically to their parent vegetable oils and as such are prone to becoming rancid. This involves autoxidation of fatty acid chains containing carbon-carbon double bonds and ultimately the formation of odoriferous, low molecular weight aldehydes, ketones and carboxylic acids. Odor is undesirable in the NOPs themselves, but more importantly, in the materials made from them.
There are a limited number of naturally occurring vegetable oils (triglycerides) which contain the unreacted hydroxyl groups that account for both the name and important reactivity of these polyols. Castor oil is the only commercially-available natural oil polyol which is produced directly from a plant source: all other NOPs require chemical modification of the oils directly available from plants.
The hope is that using renewable resources as feedstocks for chemical processes will reduce the demand on non-renewable fossil fuels currently used in the chemical industry and reduce the overall production of carbon dioxide, the most notable greenhouse gas. It has been estimated that  manufacture of NOPs produces 36% less global warming emissions (carbon dioxide), a 61% reduction in non-renewable energy use (burning fossil fuels), and a 23% reduction in the total energy demand, all relative to polyols produced from petrochemicals 

# Sources of natural oil polyols
Ninety percent of the fatty acids which make up castor oil is ricinoleic acid, which has a hydroxyl group on C-12 and a carbon-carbon double bond. The structure below shows the major component of castor oil which is composed of the tri-ester of rincinoleic acid and glycerin:
Other vegetable oils, like soy bean oil, peanut oil canola oil etc. contain carbon-carbon double bonds, but no hydroxyl groups. There are several processes used to introduce hydroxyl groups onto the carbon chain of the fatty acids, and most of these involve oxidation of the C-C double bond. Treatment of the vegetable oils with ozone cleaves the double bond, and esters or alcohols can be made, depending on the conditions used to process the ozonolysis product. The example below shows the reaction of triolein with ozone and ethylene glycol.
Air oxidation, (autoxidation), the chemistry involved in the "drying" of drying oils, gives increased molecular weight and introduces hydroxyl groups. The radical reactions involved in autoxidation can produce a complex mixture of crosslinked and oxidized triglycerides. Treatment of vegetable oils with peroxy acids gives epoxides which can be reacted with nucleophiles to give hydroxyl groups. This can be done as a one-step process. Note that in the example shown below only one of the three fatty acid chains is drawn fully, the other part of the molecule is represented by "R1" and the nucleophile is unspecified.
Triglycerides of unsaturated (containing carbon-carbon double bonds) fatty acids or methyl esters of these acids, can be treated with carbon monoxide and hydrogen in the presence of a metal catalyst to add a -CHO (formyl) groups to the chain (hydroformylation reaction) followed by hydrogenation to give the needed hydroxyl groups. In this case R1 can be the rest of the triglyceride, or a smaller group such as methyl (in which case the substrate would be similar to biodiesel). If R=Me then additional reactions like transesterification are needed to build up a polyol.

# Uses
Castor oil has found numerous  applications, many of them due to the presence of the hydroxyl group which allows chemical derivatization of the oil or modifies the properties of castor oil relative to vegetable oils which do not have the hydroxyl group. Castor oil undergoes most of the reactions that alcohols do, but the most industrially important one is reaction with diisocyanates to make polyurethanes.
Castor oil by itself has been used in making a variety of polyurethane products, ranging from coatings to foams, and the use of castor oil derivatives continues to be an area of active development. Castor oil derivatized with propylene oxide  makes polyurethane foam  for mattresses and yet another new derivative is used in coatings 
Apart from castor oil, which is a relatively expensive vegetable oil and is not produced domestically in many industrialized countries, the use of polyols derived from vegetable oils to make polyurethane products began attracting attention beginning around 2004. The rising costs of petrochemical feedstocks and an enhanced public desire for environmentally friendly green products have created a demand for these materials.. One of the most vocal supporters of these polyurethanes made using natural oil polyols is the Ford Motor Company, which announced its intentions to use polyurethane foam made using natural oil polyols in the seats of its 2008 Ford Mustang. The interest of automakers is responsible for much of the work being done on the use of NOPs in polyurethane products for use in cars, for example is seats, and headrests, armrests, soundproofing and even body panels..
NOPs are also finding use in polyurethane slab foam used to make conventional mattresses as well as memory foam mattresses.
One of the first uses for NOPs (other than castor oil) was to make spray-on polyurethane foam insulation for buildings.