Potato virus Y (PVY) is a major pathogen of potatoes and other solanaceous crops worldwide. It is most closely related to potyviruses first or only found in the Americas, and it almost certainly originated in the Andes, where its hosts were domesticated. We have inferred the phylogeny of the published genomic sequences of 240 PVY isolates collected since 1938 worldwide, but not the Andes. All fall into five groupings, which mostly, but not exclusively, correspond with groupings already devised using biological and taxonomic data. Only 42 percent of the sequences are not recombinant, and all these fall into one or other of three phylogroups; the previously named C (common), O (ordinary), and N (necrotic) groups. There are also two other distinct groups of isolates all of which are recombinant; the R-1 isolates have N (50 terminal minor) and O (major) parents, and the R-2 isolates have R-1 (major) and N (30 terminal minor) parents. Many isolates also have additional minor intra-and inter-group recombinant genomic regions. The complex interrelationships between the genomes were resolved by progressively identifying and removing recombinants using partitioned sequences of synonymous codons. Least squared dating and BEAST analyses of two datasets of gene sequences from non-recombinant heterochronously-sampled isolates (seventy-three non-recombinant major ORFs and 166 partial ORFs) found the 95% confidence intervals of the TMRCA estimates overlap around 1,000 CE (Common Era; AD). We attempted to identify the most accurate datings by comparing the estimated phylogenetic dates with historical events in the worldwide adoption of potato and other PVY hosts as crops, but found that more evidence from gene sequences of non-potato isolates, especially from South America, was required.