Potyviruses are the largest group of plant infecting RNA viruses that cause significant losses in a wide range of crops across the globe. The majority of viruses in the genus Potyvirus are transmitted by aphids in a non-persistent, non-circulative manner and have been extensively studied vis-à-vis their structure, taxonomy, evolution, diagnosis, transmission, and molecular interactions with hosts. This comprehensive review exclusively discusses potyviruses and their transmission by aphid vectors, specifically in the light of several virus, aphid and plant factors, and how their interplay influences potyviral binding in aphids, aphid behavior and fitness, host plant biochemistry, virus epidemics, and transmission bottlenecks. We present the heatmap of the global distribution of potyvirus species, variation in the potyviral coat protein gene, and top aphid vectors of potyviruses. Lastly, we examine how the fundamental understanding of these multi-partite interactions through multi-omics approaches is already contributing to, and can have future implications for, devising effective and sustainable management strategies against aphid-transmitted potyviruses to global agriculture.