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Summary: The tree of life is highly reticulate, with the history of population divergence emerging from populations of gene phylogenies that reflect histories of introgression, lineage sorting and divergence. In this study, we investigate global patterns of oak diversity and test the hypothesis that there are regions of the oak genome that are broadly informative about phylogeny.We utilize fossil data and restriction‐site associated DNA sequencing (RAD‐seq) for 632 individuals representing nearly 250 Quercus species to infer a time‐calibrated phylogeny of the world's oaks. We use a reversible‐jump Markov chain Monte Carlo method to reconstruct shifts in lineage diversification rates, accounting for among‐clade sampling biases. We then map the > 20 000 RAD‐seq loci back to an annotated oak genome and investigate genomic distribution of introgression and phylogenetic support across the phylogeny.Oak lineages have diversified among geographic regions, followed by ecological divergence within regions, in the Americas and Eurasia. Roughly 60% of oak diversity traces back to four clades that experienced increases in net diversification, probably in response to climatic transitions or ecological opportunity.The strong support for the phylogeny contrasts with high genomic heterogeneity in phylogenetic signal and introgression. Oaks are phylogenomic mosaics, and their diversity may in fact depend on the gene flow that shapes the oak genome. See also the Editorial on this article by Plomion & Martin, 226: 943–946. [ABSTRACT FROM AUTHOR]