Structural variations (SVs) such as copy number and presence–absence variations are polymorphisms that are known to impact genome composition at the species level and are associated with phenotypic variations. In the absence of a reference genome sequence, their study has long been hampered in wheat. The recent production of new wheat genomic resources has led to a paradigm shift, making possible to investigate the extent of SVs among cultivated and wild accessions. We assessed SVs affecting genes and transposable elements (TEs) in a Triticeae diversity panel of 45 accessions from seven tetraploid and hexaploid species using high-coverage shotgun sequencing of sorted chromosome 3B DNA and dedicated bioinformatics approaches. We showed that 23% of the genes are variable within this panel, and we also identified 330 genes absent from the reference accession Chinese Spring. In addition, 60% of the TE-derived reference markers were absent in at least one accession, revealing a high level of intraspecific and interspecific variability affecting the TE space. Chromosome extremities are the regions where we observed most of the variability, confirming previous hypotheses made when comparing wheat with the other grasses. This study provides deeper insights into the genomic variability affecting the complex Triticeae genomes at the intraspecific and interspecific levels and suggests a phylogeny with independent hybridization events leading to different hexaploid species.