The world’s staple food crops, and other food crops that optimize human nutrition, suffer from global virus disease pandemics and epidemics that greatly diminish their yields and/or produce quality. This situation is becoming increasingly serious because of the human population’s growing food requirements and increasing difficulties in managing virus diseases effectively arising from global warming. This review provides historical and recent information about virus disease pandemics and major epidemics that originated within different world regions, spread to other continents, and now have very wide distributions. Because they threaten food security, all are cause for considerable concern for humanity. The pandemic disease examples described are six (maize lethal necrosis, rice tungro, sweet potato virus, banana bunchy top, citrus tristeza, plum pox). The major epidemic disease examples described are seven (wheat yellow dwarf, wheat streak mosaic, potato tuber necrotic ringspot, faba bean necrotic yellows, pepino mosaic, tomato brown rugose fruit, and cucumber green mottle mosaic). Most examples involve long-distance virus dispersal, albeit inadvertent, by international trade in seed or planting material. With every example, the factors responsible for its development, geographical distribution and global importance are explained. Finally, an overall explanation is given of how to manage global virus disease pandemics and epidemics effectively.