Cultivated oat (Avena sativa L.) is an allohexaploid (AACCDD, 2n = 6x = 42) thought to have been domesticated more than 3,000 years ago while growing as a weed in wheat, emmer and barley fields in Anatolia1,2. Oat has a low carbon footprint, substantial health benefits and the potential to replace animal-based food products. However, the lack of a fully annotated reference genome has hampered efforts to deconvolute its complex evolutionary history and functional gene dynamics. Here we present a high-quality reference genome of A. sativa and close relatives of its diploid (Avena longiglumis, AA, 2n = 14) and tetraploid (Avena insularis, CCDD, 2n = 4x = 28) progenitors. We reveal the mosaic structure of the oat genome, trace large-scale genomic reorganizations in the polyploidization history of oat and illustrate a breeding barrier associated with the genome architecture of oat. We showcase detailed analyses of gene families implicated in human health and nutrition, which adds to the evidence supporting oat safety in gluten-free diets, and we perform mapping-by-sequencing of an agronomic trait related to water-use efficiency. This resource for the Avena genus will help to leverage knowledge from other cereal genomes, improve understanding of basic oat biology and accelerate genomics-assisted breeding and reanalysis of quantitative trait studies.