The family Geminiviridae comprises a group of plant-infecting circular ssDNA viruses that severely constrain agricultural production throughout the temperate regions of the world, and are a particularly serious threat to food security in sub-Saharan Africa. While geminiviruses exhibit considerable diversity in terms of their nucleotide sequences, genome structures, host ranges and insect vectors, the best characterised and economically most important of these viruses are those in the genus Begomovirus. Whereas begomoviruses are generally considered to be either monopartite (one ssDNA component) or bipartite (two circular ssDNA components called DNA-A and DNA-B), many apparently monopartite begomoviruses are associated with additional subviral ssDNA satellite components, called alpha- (DNA-αs) or betasatellites (DNA-βs). Additionally, subgenomic molecules, also known as defective interfering (DIs) DNAs that are usually derived from the parent helper virus through deletions of parts of its genome, are also associated with bipartite and monopartite begomoviruses. The past three decades have witnessed the emergence and diversification of various new begomoviral species and associated DI DNAs, in southern Africa, East Africa, and proximal Indian Ocean islands, which today threaten important vegetable and commercial crops such as, tobacco, cassava, tomato, sweet potato, and beans. This review aims to describe what is known about these viruses and their impacts on sustainable production in this sensitive region of the world.