13C nuclear magnetic resonance spectroscopy has been successfully applied to determine the structures of natural derivatives of long-chain fatty acids and in particular, waxes and glycerides. The term wax is used to indicate esters of aliphatic acids with alcohols other than glycerol. 13C chemical shifts of unsaturated carbons in long-chain esters and acids were explained in terms of long-range σ-inductive interactions through saturated C-C bonds in polymethylene chains. A mathematical model was proposed to predict NMR shifts at sp2 carbons of mono- and non-conjugated polyenoic acids and esters. 13C NMR was also applied for studying the structure of glycerides. Unsaturation degree, cis-trans isomerization, and positional isomerism of fatty acids were determined along with their distribution between the 1,3- and 2-positions of glycerol backbone. The compositional data of the two fatty acid pools which esterify 1,3- and 2-glycerol positions, opened a new frontier in the knowledge of glyceride structures. Positional data of triglycerides enabled the set-up of new analytical methodologies which apply quantitative 13C NMR spectroscopy to determine the composition of natural mixtures of triacylglycerols, i.e. vegetable oils.