The existence of vestigial structures is one of the main lines of evidence for macroevolution. Here I introduce a phylogenetic bracketing approach to the identification of vestigial structures and apply it to Dinosauria. According to this approach, a structure is considered vestigial if, in comparison with its homolog in at least three successive outgroups, it is reduced to one‐third or less its size relative to adjacent structures and if at least distally it has lost the specialized morphology present in the three outgroups. This approach identifies fingers IV and V as vestigial in dinosaurs in general, II–V in sauropods, III in Tyrannosauridae and Caudipteryx, II and III in Shuvuuia and I and III in modern birds. The entire forelimb distal to the elbow is vestigial in Abelisauridae. Vestigial parts of the pelvic girdle and hindlimb include the pubic shaft in Iguanodontia and Ceratopsia, the entire pubis in Ankylosauria, the first metatarsal in derived Iguanodontia, the first metatarsal shaft in Theropoda and the fifth toe in dinosaurs in general. Derived Centrosaurinae and some Chasmosaurus exhibit vestigial supraorbital horns. Some centrosaurines have a vestigial nasal horn. The antorbital cavity is vestigial in Thyreophora, Iguanodontia and Ceratopsidae. I recommend that this information be exploited to increase public awareness of the evidence for macroevolution.