The Fagopyrum genus includes two cultivated species, namely common buckwheat (F. esculentum Moench) and Tartary buckwheat (F. tataricum Gaertn.), and more than 25 wild buckwheat species. The goal of breeders is to improve the properties of cultivated buckwheat with methods of classical breeding, with the support of biotechnological methods or a combination of both. In this paper, we reviewed the possibility to use transcriptomics, genomics, interspecific hybridization, tissue cultures and plant regeneration, molecular markers, genetic transformation, and genome editing to aid in both the breeding of buckwheat and in the identification and production of metabolites important for preserving human health. The key problems in buckwheat breeding are the unknown mode of inheritance of most traits, associated with crop yield and the synthesis of medicinal compounds, low seed yield, shedding of seeds, differential flowering and seed set on branches, and unknown action of genes responsible for the synthesis of buckwheat metabolites of pharmaceutical and medicinal interest.