The end-use value of bread wheat (Triticum aestivum L.) grain is mainly determined by grain storage protein (GSP) content and composition. Glutenins and gliadins are the two main classes of GSPs in wheat. They are produced by genes mainly controlled at the transcriptional level by a network involving at least eight transcription factors (TFs). This network could lead to the stable allometric scaling relationships observed between the quantity of GSPs, gliadins or glutenins and the total quantity of nitrogen (N) per grain. Chromosomic regions involved in GSP accumulation, composition and allometric grain N allocation were identified using linkage mapping in 196 accessions of a bread wheat worldwide core collection grown in three environments. We used 873 markers for genome-wide association and 167 single nucleotide polymorphism markers in 51 candidate genes, including 35 TFs expressed in the grain, for candidate association. We identified 95 associated loci, 29 (31%) of which were inside or in strong linkage disequilibrium with candidate genes. As expected, structural GSP genes were associated with studied traits. In addition, several loci putatively trans-regulating GSP accumulation were uncovered. Seven candidate TFs were associated or in strong linkage disequilibrium with markers associated with the composition or quantity of glutenin or gliadin, or allometric grain N allocation parameters, confirming the importance of the transcriptional control of GSP accumulation. Our results suggest that the genetic determinants of glutenin and gliadin compositions are mostly distinct from each other.