Biological invasions affect virtually all ecosystems on earth, but the degree to which different regions and biomes are invaded, and the quality of information from different regions, varies greatly. A large body of literature exists on the invasion of savannas in the Neotropics and northern Australia where invasive plants, especially African grasses, have had major impacts. Less has been published on plant invasions in African savannas, except for those in South Africa. Negative impacts due to plant invasions in African savannas appear to be less severe than in other regions at present. As savannas cover about 60% of the continent, with tens of millions of people relying on the services they provide, it is timely to assess the current status of invasions as a threat to these ecosystems. We reviewed the literature, contrasting the African situation with that of Neotropical and Australian savannas. A number of drivers and explanatory factors of plant invasions in savannas have been described, mostly from the Neotropics and Australia. These include herbivore presence, residence time, intentional introductions for pasture improvements, fire regimes, the physiology of the introduced species, and anthropogenic disturbance. After comparing these drivers across the three regions, we suggest that the lower extent of alien plant invasions in African savannas is largely attributable to: (1) significantly lower rates of intentional plant introductions and widespread plantings (until recently); (2) the role of large mammalian herbivores in these ecosystems; (3) historical and biogeographical issues relating to the regions of origin of introduced species; and (4) the adaptation of African systems to fire. We discuss how changing conditions in the three regions are likely to affect plant invasions in the future.