We review half a century of research on Cucumis melo resistance to Aphis gossypii from molecular to field levels. The Vat gene is unique in conferring resistance to both A. gossypii and the viruses it transmits. This double phenotype is aphid clone-dependent and has been observed in 25 melon accessions, mostly from Asia. It is controlled by a cluster of genes including CC-NLR, which has been characterized in detail. Copy-number polymorphisms (for the whole gene and for a domain that stands out in the LLR region) and single-nucleotide polymorphisms have been identified in the Vat cluster. The role of these polymorphisms in plant/aphid interactions remains unclear. The Vat gene structure suggests a functioning with separate recognition and response phases. During the recognition phase, the VAT protein is thought to interact (likely indirectly) with an aphid effector introduced during cell puncture by the aphid. A few hours later, several miRNAs are upregulated in Vat plants. Peroxidase activity increases, and callose and lignin are deposited in the walls of the cells adjacent to the stylet path, disturbing aphid behavior. In aphids feeding on Vat plants, Piwi-interacting RNA-like sequences are abundant and the levels of other miRNAs are modified. At the plant level, resistance to aphids is quantitative (aphids escape the plant and display low rates of reproduction). Resistance to viruses is qualitative and local. Durability of NLR genes is highly variable. A. gossypii clones are adapted to Vat resistance, either by introducing a new effector that interferes with the deployment of plant defenses, or by adapting to the defenses it triggered. Viruses transmitted in a non-persistent manner cannot adapt to Vat resistance. At population level, Vat reduces aphid density and genetic diversity. The durability of Vat resistance to A. gossypii populations depends strongly on the agro-ecosystem, including, in particular, the presence of other cucurbit crops serving as alternative hosts for adapted clones in fall and winter. At the crop level, Vat resistance decreases the intensity of virus epidemics when A. gossypii is the main aphid vector in the crop environment.