Plant viruses are responsible for the most devastating and commercially significant plant diseases, especially in tropical and subtropical regions. The genus begomovirus is the largest one in the family Geminiviridae, with a single-stranded DNA genome, either monopartite or bipartite. Begomoviruses are transmitted by insect vectors, such as Bemisia tabaci. Begomoviruses are the major causative agents of diseases in agriculture globally. Because of their diversity and mode of evolution, they are thought to be geographic specific. The emerging begomoviruses are of serious concern due to their increasing host range and geographical expansion. Several begomoviruses of Asiatic origin have been reported in Europe, causing massive economic losses; insect-borne transmission of viruses is a critical factor in virus outbreaks in new geographical regions. This review highlights crucial information regarding Asia’s four emerging and highly destructive begomoviruses. We also provided information regarding several less common but still potentially important pathogens of different crops. This information will aid possible direction of future studies in adopting preventive measures to combat these emerging viruses.