Background: Canine rabies causes many thousands of human deaths every year in Africa, and continues to increase throughout much of the continent. Methodology/Principal Findings: This paper identifies four common reasons given for the lack of effective canine rabies control in Africa: (a) a low priority given for disease control as a result of lack of awareness of the rabies burden; (b) epidemiological constraints such as uncertainties about the required levels of vaccination coverage and the possibility of sustained cycles of infection in wildlife; (c) operational constraints including accessibility of dogs for vaccination and insufficient knowledge of dog population sizes for planning of vaccination campaigns; and (d) limited resources for implementation of rabies surveillance and control. We address each of these issues in turn, presenting data from field studies and modelling approaches used in Tanzania, including burden of disease evaluations, detailed epidemiological studies, operational data from vaccination campaigns in different demographic and ecological settings, and economic analyses of the cost-effectiveness of dog vaccination for human rabies prevention. Conclusions/Significance: We conclude that there are no insurmountable problems to canine rabies control in most of Africa; that elimination of canine rabies is epidemiologically and practically feasible through mass vaccination of domestic dogs; and that domestic dog vaccination provides a cost-effective approach to the prevention and elimination of human rabies deaths.