Aegilops tauschii Coss., the D genome donor of hexaploid wheat (Triticum aestivum L.), is the most promising resource used to broaden the genetic diversity of wheat. Taxonomical studies have classified Ae. tauschii into two subspecies, ssp. tauschii and ssp. strangulata. However, molecular analysis revealed three distantly related lineages, TauL1, TauL2 and TauL3. TauL1 and TauL3 includes the only ssp. tauschii, whereas TauL2 includes both subspecies. This study aimed to clarify the phylogeny of Ae. tauschii and to find the traits that can differentiate between TauL1, TauL2 and TauL3, or between ssp. tauschii and ssp. strangulata. We studied the genetic and morpho-physiological diversity in 293 accessions of Ae. tauschii, covering the entire range of the species. A total of 5880 high-quality SNPs derived from DArTseq were used for phylogenetic cluster analyses. As a result, we observed wide morpho-physiological variation in each lineage and subspecies. Despite this variation, no key traits can discriminate lineages or subspecies though some traits were significantly different. Of 124 accessions previously lacking the passport data, 66 were allocated to TauL1, 57 to TauL2, and one to TauL3.