Banana and plantain (Musa spp.), produced in 10.3 million ha in the tropics, are among the world's top 10 food crops. They are vegetatively propagated using suckers or tissue culture plants and grown almost as perennial plantations. These are prone to the accumulation of pests and pathogens, especially viruses which contribute to yield reduction and are also barriers to the international exchange of germplasm. The most economically important viruses of banana and plantain are Banana bunchy top virus (BBTV), a complex of banana streak viruses (BSVs) and Banana bract mosaic virus (BBrMV). BBTV is known to cause the most serious economic losses in the "Old World," contributing to a yield reduction of up to 100% and responsible for a dramatic reduction in cropping area. The BSVs exist as episomal and endogenous forms are known to be worldwide in distribution. In India and the Philippines, BBrMV is known to be economically important but recently the virus was discovered in Colombia and Costa Rica, thus signaling its spread into the "New World." Banana and plantain are also known to be susceptible to five other viruses of minor significance, such as Abaca mosaic virus, Abaca bunchy top virus, Banana mild mosaic virus, Banana virus X, and Cucumber mosaic virus. Studies over the past 100 years have contributed to important knowledge on disease biology, distribution, and spread. Research during the last 25 years have led to a better understanding of the virus-vector-host interactions, virus diversity, disease etiology, and epidemiology. In addition, new diagnostic tools were developed which were used for surveillance and the certification of planting material. Due to a lack of durable host resistance in the Musa spp., phytosanitary measures and the use of virus-free planting material are the major methods of virus control. The state of knowledge on BBTV, BBrMV, and BSVs, and other minor viruses, disease spread, and control are summarized in this review.