There are two families of EFAs: ω-3 (or omega-3 or n−3) and ω-6 (omega-6, n−6). Fats from each of these families are essential, as the body can convert one omega-3 to another omega-3, for example, but cannot create an omega-3 from scratch. They were originally designated as Vitamin F when they were discovered as essential nutrients in 1923. In 1930, work by Burr, Burr and Miller showed that they are better classified with the fats than with the vitamins.
These two fatty acids cannot be synthesised by humans, as humans lack the desaturase enzymes required for their production.
They form the starting point for the creation of longer and more desaturated fatty acids, which are also referred to as long-chain polyunsaturated fatty acids (LC-PUFA):
ω-9 fatty acids are not essential in humans, because humans generally possess all the enzymes required for their synthesis. Exceptions do occur in older people or people with a liver problem that do not completely produce a sufficient amount, and hence many supplement companies market Omega 3-6-9 blends.
Traditionally speaking the LC-PUFA are not essential. See (Cunnane 2003) for a discussion of the current status of the term 'essential'. Because the LC-PUFA are sometimes required, they may be considered "conditionally essential", or not essential to healthy adults.
Mary G. Enig has pointed out numerous studies showing the need for omega-3 and omega-6 essential fatty acids in mammalians A 2005 study has shown evidence that gamma-linolenic acid, GLA, a product of omega-6, has been shown to inhibit the breast cancer promoting gene of Her2/neu.
Biologist Ray Peat has pointed out flaws in the studies purportedly showing the need for n-3 and n-6 fats. He notes that so-called EFA deficiencies have sometimes been reversed by adding B vitamins or a fat-free liver extract to the diet. In his view, 'the optional dietary level of the "essential fatty acids" might be close to zero, if other dietary factors were also optimized.' 
Essential fatty acids should not be confused with essential oils, which are "essential" in the sense of being a concentrated essence.
Essential fatty acids play a part in many metabolic processes, and there is evidence to suggest that low levels of essential fatty acids, or the wrong balance of types among the essential fatty acids, may be a factor in a number of illnesses, including osteoporosis.
Plant sources of ω-3 contain neither eicosapentaenoic acid (EPA) nor docosahexaenoic acid (DHA). The human body can (and in case of a purely vegetarian diet often must, unless certain algae or supplements derived from them are consumed) convert α-linolenic acid (ALA) to EPA and subsequently DHA. This however requires more metabolic work, which is thought to be the reason that the absorption of essential fatty acids is much greater from animal rather than plant sources (see Fish and plants as a source of Omega-3 for more).
The provides a very large and detailed listing of fat contents of animal and vegetable fats, including ω-3 and -6 oils. The National Institutes of Health's EFA Education group publishes 'Essential Fats in Food Oils.' This lists 40 common oils, more tightly focused on EFAs and sorted by n-6:3 ratio. list notable vegetable sources of EFAs as well as commentary and an overview of the biosynthetic pathways involved. Users can interactively search at Nutrition Data for the richest food sources of particular EFAs or other nutrients. Careful readers will note that these sources are not in excellent agreement. EFA content of vegetable sources varies with cultivation conditions. Animal sources vary widely, both with the animal's feed and that the EFA makeup varies markedly with fats from different body parts.