Cassava (Manihot esculenta Crantz.) is the most important vegetatively propagated food staple in Africa and a prominent industrial crop in Latin America and Asia. Its vegetative propagation through stem cuttings has many advantages, but deleteriously it means that pathogens are passed from one generation to the next and can easily accumulate, threatening cassava production. Cassava-growing continents are characterized by specific suites of viruses that affect cassava and pose particular threats. Of major concern, causing large and increasing economic impact in Africa and Asia are the cassava mosaic geminiviruses that cause cassava mosaic disease in Africa and Asia and cassava brown streak viruses causing cassava brown streak disease in Africa. Latin America, the center of origin and domestication of the crop, hosts a diverse set of virus species, of which the most economically important give rise to cassava frog skin disease syndrome. Here, we review current knowledge on the biology, epidemiology, and control of the most economically important groups of viruses in relation to both farming and cultural practices. Components of virus control strategies examined include: diagnostics and surveillance, prevention and control of infection using phytosanitation, and control of disease through the breeding and promotion of varieties that inhibit virus replication and/or movement. We highlight areas that need further research attention and conclude by examining the likely future global outlook for virus disease management in cassava.