Impacts of predators on prey populations are incurred not only through mortality inflicted, but also from how the risk of mortality affects the behaviour, spatial distribution and resource access of potential prey species. This risk is governed by exposure to predators and vulnerability following encounters. Behavioural responses to reduce risks have ramifying consequences for habitat partitioning, regional distributions and local impacts of herbivores on vegetation. These consequences are reviewed for carnivore-ungulate assemblages in African savanna ecosystems. Vigilance serves multiple functions, including locating food and maintaining group cohesion as well as detecting predators. Prey responses depend on whether predators hunt by ambush or pursuit and whether they are mainly diurnally or nocturnally active. Ungulates can lower their vulnerability by restricting time spent foraging at night and avoid places providing cover for lurking carnivores. Risks of predation can have a stronger influence on spatial partitioning among large grazers than distinctions in resource use. Only species above some threshold size have distributions indifferent to tree and grass cover. Observed mortality rates are constrained by recruitment potential. Spatiotemporal variation in risk may regulate populations and limit regional abundance. Herbivores confined to secure habitat may generate local brown-green-black world mosaics. Less common prey species of greatest conservation concern are most susceptible to having their habitat security breached by changes in predation risk. Studies establishing baseline responses of ungulates to the risk of predation need to be augmented by investigations focussed on extreme situations.