Vegetable oils are important components of the human diet, and are also actively used for industrial and cosmetic purposes and as biofuels. The scope of oil application largely depends on its composition. The fatty acid composition of oils, in its turn, is built upon the presence and activity of the enzymes of their biosynthesis. The presented review is an attempt to summarize and generalize information on the genetic control of fatty acid synthesis and the range of natural variation in their composition in key oilseed crops: peanut (Arachis hypogaea L.), sunflower (Helianthus annuus L.), flax (Linum usitatissimum L.), rapeseed (Brassica napus L.), camelina (Camelina sativa L.), cotton (Gossypium hirsutum L.), safflower (Carhtamus tinctorius L.), castor bean (Ricinus communis L.) etc., as well as approaches to changing the fatty acid percentage in plants, including gene silencing, overexpression of genes for the synthesis of fatty acids, changing the pattern of their expression, and genome editing.