Background. Introgressive events (e.g., hybridization, gene flow, horizontal gene transfer) and incomplete lineage sorting of ancestral polymorphisms are a challenge for phylogenetic analyses since different genes may exhibit conflicting genealogical histories. Grasses of the Triticeae tribe provide a particularly striking example of incongruence among gene trees. Previous phylogenies, mostly inferred with one gene, are in conflict for several taxon positions. Therefore, obtaining a resolved picture of relationships among genera and species of this tribe has been a challenging task. Here, we obtain the most comprehensive molecular dataset to date in Triticeae, including one chloroplastic and 26 nuclear genes. We aim to test whether it is possible to infer phylogenetic relationships in the face of (potentially) large-scale introgressive events and/or incomplete lineage sorting; to identify parts of the evolutionary history that have not evolved in a tree-like manner; and to decipher the biological causes of gene-tree conflicts in this tribe. Results: We obtain resolved phylogenetic hypotheses using the supermatrix and Bayesian Concordance Factors (BCF) approaches despite numerous incongruences among gene trees. These phylogenies suggest the existence of 4-5 major clades within Triticeae, with Psathyrostachys and Hordeum being the deepest genera. In addition, we construct a multigenic network that highlights parts of the Triticeae history that have not evolved in a tree-like manner. Dasypyrum, Heteranthelium and genera of clade V, grouping Secale, Taeniatherum, Triticum and Aegilops, have evolved in a reticulated manner. Their relationships are thus better represented by the multigenic network than by the supermatrix or BCF trees. Noteworthy, we demonstrate that gene-tree incongruences increase with genetic distance and are greater in telomeric than centromeric genes. Together, our results suggest that recombination is the main factor decoupling gene trees from multigenic trees. Conclusions: Our study is the first to propose a comprehensive, multigenic phylogeny of Triticeae. It clarifies several aspects of the relationships among genera and species of this tribe, and pinpoints biological groups with likely reticulate evolution. Importantly, this study extends previous results obtained in Drosophila by demonstrating that recombination can exacerbate gene-tree conflicts in phylogenetic reconstructions