Among the most serious problems in papaya production are the viruses associated with papaya ringspot and papaya sticky disease (PSD). PSD concerns producers worldwide because its symptoms are extremely aggressive and appear only after flowering. As no resistant cultivar is available, several disease management strategies have been used in affected countries, such as the use of healthy seeds, exclusion of the pathogen, and roguing. In the 1990s, a dsRNA virus, papaya meleira virus (PMeV), was identified in Brazil as the causal agent of PSD. However, in 2016 a second virus, papaya meleira virus 2 (PMeV2), with an ssRNA genome, was also identified in PSD plants. Only PMeV is detected in asymptomatic plants, whereas all symptomatic plants contain both viral RNAs separately packaged in particles formed by the PMeV capsid protein. PSD also affects papaya plants in Mexico, Ecuador, and Australia. PMeV2-like viruses have been identified in the affected plants, but the partner virus(es) in these countries are still unknown. In Brazil, PMeV and PMeV2 reside in laticifers that promote spontaneous latex exudation, resulting in the affected papaya fruit’s sticky appearance. Genes modulated in plants affected by PSD include those involved in reactive oxygen species and salicylic acid signaling, proteasomal degradation, and photosynthesis, which are key plant defenses against PMeV complex infection. However, the complete activation of the defense response is impaired by the expression of negative effectors modulated by the virus. This review presents a summary of the current knowledge of the Carica papaya-PMeV complex interaction and management strategies.