Papaya leaf curl disease (PaLCuD) caused by papaya leaf curl virus (PaLCuV) not only affects yield but also plant growth and fruit size and quality of papaya and is one of the most damaging and economically important disease. Management of PaLCuV is a challenging task due to diversity of viral strains, the alternate hosts, and the genomic complexities of the viruses. Several management strategies currently used by plant virologists to broadly control or eliminate the viruses have been discussed. In the absence of such strategies in the case of PaLCuV at present, the few available options to control the disease include methods like removal of affected plants from the field, insecticide treatments against the insect vector (Bemisia tabaci), and gene-specific control through transgenic constructs. This review presents the current understanding of papaya leaf curl disease, genomic components including satellite DNA associated with the virus, wide host and vector range, and management of the disease and suggests possible generic resistance strategies.