Oat (Avena sativa L.) is an important and nutritious cereal crop, and there is a growing need to identify genes that contribute to improved oat varieties. Here we utilize a newly sequenced and annotated oat reference genome to locate and characterize quantitative trait loci (QTLs) affecting agronomic and grain-quality traits in five oat populations. We find strong and significant associations between the positions of candidate genes and QTL that affect heading date, as well as those that influence the concentrations of oil and β-glucan in the grain. We examine genome-wide recombination profiles to confirm the presence of a large, unbalanced translocation from chromosome 1 C to 1 A, and a possible inversion on chromosome 7D. Such chromosome rearrangements appear to be common in oat, where they cause pseudo-linkage and recombination suppression, affecting the segregation, localization, and deployment of QTLs in breeding programs.