Insect-transmitted viruses cause some of the most damaging and economically important diseases of crop plants, especially in tropical and subtropical regions. The geminiviruses, a group of single-stranded DNA viruses with unique twined icosahedral virus particles, are responsible for many of these diseases. Of particular importance are the geminiviruses transmitted by whiteflies (Bemisia tabaci), which are in the genus Begomovirus. This is the largest genus of plant viruses (in terms of number of species), and some are responsible for devastating diseases in vegetable and fiber crops throughout the world. This review presents the current understanding of begomoviruses, the diseases they cause, and approaches for disease management. An emphasis is placed on the most important begomovirus diseases in Brazil, which are those that affect common bean and tomato. However, because of the wide host range of the vector and the genetic flexibility of begomoviruses, these diseases pose a threat to many other crops. Therefore, the current situation with begomoviruses that infect okra, pepper, potato, sweet potato and soybean in Brazil is also discussed.