Grasses inhabit the Earth in greater abundance and distribution than any other group of plants, with representatives colonizing every continent on the planet, from the littoral zone to the highest alpine region, and from equatorial rainforests to the highest northern or southern latitudes (Gould and Shaw, 1983). Grasses have many roles in their ecosystems, including primary colonization and forages for a wide variety of grazing animals and insects. Further, their root systems act to build and bind soils and the minerals therein. Humans depend very heavily on the grass family, and domestication of grasses underpinned the origins of agricultural civilizations in the Near East, Asia, and Americas. Grains of many grasses form staple food supplies for humankind, while others are used as forage for both domesticated and wild animals. The fundamental importance of the grasses has prompted efforts to develop a framework within which we can classify them and summarize their evolutionary relationships. As will be shown below, grasses do not conform well to the rules of orthodox taxonomy. They often do not form groups of similar populations (species) separated from one another by sharp, easily recognizable gaps (Stebbins, 1972). Many interfertile grasses exhibit striking morphological variation, and others that appear very similar are incapable of interbreeding. Some groups of grasses show extensive hybridization, which results in a complex reticulating web of relationships rather than simple linear pedigrees. Other species are agamospermic; that is, they reproduce entirely without the usual sexual processes. These conflicts have thrown grass taxonomy into a state of flux, with characterization of species being highly dependant on the criteria used. Yet, significant progress has been made to develop a classification framework for the grasses using a variety of criteria.