The genus Utricularia includes around 250 species of carnivorous plants, commonly known as bladderworts. The generic name Utricularia was coined by Carolus Linnaeus in reference to the carnivorous organs (Utriculus in Latin) present in all species of the genus. Since the formal proposition by Linnaeus, many species of Utricularia were described, but only scarce information about the biology for most species is known. All Utricularia species are herbs with vegetative organs that do not follow traditional models of morphological classification. Since the formal description of Utricularia in the 18th century, the trap function has intrigued naturalists. Historically, the traps were regarded as floating organs, a common hypothesis that was maintained by different botanists. However, Charles Darwin was most likely the first naturalist to refute this idea, since even with the removal of all traps, the plants continued to float. More recently, due mainly to methodological advances, detailed studies on the trap function and mechanisms could be investigated. This review shows a historical perspective on Utricularia studies which focuses on the traps and body organization.