Common buckwheat (Fagopyrum esculentum) is an important non-cereal grain crop and a prospective component of functional food. Despite this, the genomic resources for this species and for the whole family Polygonaceae, to which it belongs, are scarce. Here, we report the assembly of the buckwheat genome using long-read technology and a high-resolution expression atlas including 46 organs and developmental stages. We found that the buckwheat genome has an extremely high content of transposable elements, including several classes of recently (0.5–1 Mya) multiplied TEs (“transposon burst”) and gradually accumulated TEs. The difference in TE content is a major factor contributing to the three-fold increase in the genome size of F. esculentum compared with its sister species F. tataricum. Moreover, we detected the differences in TE content between the wild ancestral subspecies F. esculentum ssp. ancestrale and buckwheat cultivars, suggesting that TE activity accompanied buckwheat domestication. Expression profiling allowed us to test a hypothesis about the genetic control of petaloidy of tepals in buckwheat. We showed that it is not mediated by B-class gene activity, in contrast to the prediction from the ABC model. Based on a survey of expression profiles and phylogenetic analysis, we identified the MYB family transcription factor gene tr_18111 as a potential candidate for the determination of conical cells in buckwheat petaloid tepals. The information on expression patterns has been integrated into the publicly available database TraVA: http://travadb.org/browse/Species=Fesc/. The improved genome assembly and transcriptomic resources will enable research on buckwheat, including practical applications.