Lipoxygenases (LOX) and cyclooxygenases (COX) react an achiral polyunsaturated fatty acid with oxygen to form a chiral peroxide product of high regio- and stereochemical purity. Both enzymes employ free radical chemistry reminiscent of hydrocarbon autoxidation but execute efficient control during catalysis to form a specific product over the multitude of isomers found in the nonenzymatic reaction. Exactly how both dioxygenases achieve this positional and stereo control is far from clear. We present four mechanistic models, not mutually exclusive, that could account for the specific reactions of molecular oxygen with a fatty acid in the LOX or COX active site.