Abstract. Several tick species, in what is now known as the subgenus Boophilus in the genusRhipicephalus, are economically important ectoparasites of livestock and other ungulates; as vectors of pathogens that kill cattle, they remain among the most studied ticks in the world. Researchers have developed quantitative computer models of Rhipicephalus ticks since the early 1970s to study complex biological and ecological relationships that influence management or eradication of ticks and tick-borne diseases. We review the 45-yr history of Rhipicephalus (Boophilus) models, which were developed and applied first in Australia, 10 yr later in North and South America, then soon after in Africa. Models progressed from analytical models of a portion of tick life cycles, to simulation models of complete life cycles or ecoclimatic indices, to the current emphasis on GIS-based bioclimatic envelope models estimated from remotely sensed data and tick presence records. Earlier models were used primarily to predict effects of management techniques, such as use of sterile hybrid ticks, pasture rotation, acaricides, vaccines, and resistant cattle, while more recent models have been used to predict the potential for range expansion, especially due to global climate change and wildlife hosts, as well as in the face of competition with other tick species. We summarize characteristics of these models and compare those of population dynamics and bioclimatic envelope models. We discuss the past and present utility of these models and provide a perspective on future Rhipicephalus (Boophilus) modeling efforts.