High-molecular-weight glutenin subunits (HMW-GS) encoded by alleles at the <em>Glu-A1</em>, <em>Glu-B1</em>, and <em>Glu-D1</em> loci confer unique bread-making properties of common wheat (<em>Triticum aestivum</em> L.). The identification of HMW-GS is the prerequisite for pyramiding high-quality glutenin genes. The present review is designed to list all published HMW-GS alleles in <em>Triticum</em> species and triticale (A- and B genomes), focusing on methods for their identification. <em>T. monococcum</em> is characterized by 37 alleles at the <em>Glu-1</em> locus versus four alleles in <em>T. thaoudar</em> and 39 in <em>T. urartu</em>. In total, 80 alleles at <em>Glu-A1</em> of diploid <em>Triticum</em> species and about 42 alleles found in polyploid wheat landraces and varieties (4x and 6x), including triticale, were listed. Allelic variation at the <em>Glu-B1</em> locus is divided into 3 groups: <em>a</em> – <em>z</em>, <em>aa</em> – <em>az</em>, and <em>ba</em> – <em>ct</em>, comprising 121 alleles, of which 26 subunits have unspecified alleles. At least 51 allelic variants at locus <em>Glu-D1</em> of <em>Triticum</em> species were indicated, along with carriers of the species level. In addition, subunit-specific genetic loci have been tagged, facilitating molecular marker development of high-gluten wheat cultivars through marker-assisted breeding.