Givnish earned his PhD at Princeton in 1976, and then taught at Harvard before joining the faculty at the University of Wisconsin-Madison in 1985. He is an elected Fellow of the American Association for the Advancement of Science, and an elected Fellow of the Linnean Society of London. He has published more than 140 papers and edited two books.
Givnish is known for his research on the functional and ecological significance of several aspects of plant form and physiology related to energy capture, and for his use molecular systematics as a basis for studying patterns of adaptive radiation, geographic spread, and species diversification in several plant lineages, especially those on oceanic islands and tropical mountains. He has conducted ecological and evolutionary studies in several parts of North America, South America, Australia, and the Pacific Basin. He is an expert on the phylogeny and biogeography of several monocot families (bromeliads, rapateads, lilies, orchids, and their relatives), and has made several contributions to the study of carnivorous plants, including the discovery of carnivory in bromeliads native to the tepuis of southern Venezuela, and the creation of a cost-benefit model for the evolution of carnivory.