Did the end-Cretaceous mass extinction event, by eliminating non-avian dinosaurs and most of the existing fauna, trigger the evolutionary radiation of present-day mammals? Here we construct, date and analyse a species-level phylogeny of nearly all extant Mammalia to bring a new perspective to this question. Our analyses of how extant lineages accumulated through time show that net per-lineage diversification rates barely changed across the Cretaceous/Tertiary boundary. Instead, these rates spiked significantly with the origins of the currently recognized placental superorders and orders approximately 93 million years ago, before falling and remaining low until accelerating again throughout the Eocene and Oligocene epochs. Our results show that the phylogenetic 'fuses' leading to the explosion of extant placental orders are not only very much longer than suspected previously, but also challenge the hypothesis that the end-Cretaceous mass extinction event had a major, direct influence on the diversification of today's mammals. Molecular data and the fossil record can give conflicting views of the evolutionary past. For instance, empirical palaeontological evidence by itself tends to favour the 'explosive model' of diversification for extant placental mammals 1 , in which the orders with living representatives both originated and rapidly diversified soon after the Cretaceous/Tertiary (K/T) mass extinction event that eliminated non-avian dinosaurs and many other, mostly marine 2 , taxa 65.5 million years (Myr) ago 1,3,4. By contrast, molecular data consistently push most origins of the same orders back into the Late Cretaceous period 5-9 , leading to alternative scenarios in which placental line-ages persist at low diversity for some period of time after their initial origins ('phylogenetic fuses'; see ref. 10) before undergoing evolutionary explosions 1,11. Principal among these scenarios is the 'long-fuse model' 1 , which postulates an extended lag between the Cretaceous origins of the orders and the first split among their living representatives (crown groups) immediately after the K/T boundary 8. Some older molecular studies advocate a 'short-fuse model' of diversification 1 , where even the basal crown-group divergences within some of the larger placental orders occur well within the Cretaceous period 5-7. A partial molecular phylogeny emphasizing divergences among placental orders suggested that over 20 lineages with extant descendants (henceforth, 'extant lineages') survived the K/T boundary 8. However, the total number of extant lineages that pre-date the extinction event and whether or not they radiated immediately after it remain unknown. The fossil record alone does not provide direct answers to these questions. It does reveal a strong pulse of diversification in stem eutherians immediately after the K/T boundary 4,12 , but few of the known Palaeocene taxa can be placed securely within the crown groups of extant orders comprising Placentalia 4. The latter only rise to prominence in fossils known from the Early Eocene epoch onwards (,50 Myr ago) after a major faunal reorganization 4,13,14. The geographical patchiness of the record complicates interpretations of this near-absence of Palaeocene crown-group fossils 14-16 : were these clades radiating throughout the Palaeocene epoch in parts of the world where the fossil record is less well known; had they not yet originated; or did they have very long fuses, remaining at low diversity until the major turnover at the start of the Eocene epoch? The pattern of diversification rates through time, to which little attention has been paid so far, might hold the key to answering these questions. If the Cretaceous fauna inhibited mammalian diversification , as is commonly assumed 1 , and all mammalian lineages were able to radiate after their extinction, then there should be a significant increase in the net per-lineage rate of extant mammalian diversification , r (the difference between the per-lineage speciation and extinction rates), immediately after the K/T mass extinction. This hypothesis, along with the explosive, long-and short-fuse models, can be tested using densely sampled phylogenies of extant species, which contain information about the history of their diversification rates 17-20. Using modern supertree algorithms 21,22 , we construct the first virtually complete species-level phylogeny of extant mammals from over 2,500 partial estimates, and estimate divergence times (with confidence intervals) throughout it using a 66-gene alignment in conjunction with 30 cladistically robust fossil calibration points. Our analyses of the supertree indicate that the principal splits underlying the diversification of the extant lineages occurred (1) from 100-85 Myr ago with the origins of the extant orders, and (2) in or after the Early Eocene (agreeing with the upturn in their diversity known from the fossil record 4,13,14), but not immediately after the K/T boundary, where diversification rates are unchanged. Our findings-that more extant placental lineages survived the K/T boundary than previously recognized and that fewer arose immediately after it than previously suspected-extend the phylogenetic fuses of many extant orders and indicate that the end-Cretaceous mass extinction event had, at best, a minor role in driving the diversification of the present-day mam-malian lineages. A supertree with divergence times for extant mammals The supertree contains 4,510 of the 4,554 extant species recorded in ref. 23, making it 99.0% complete at the species level (Fig. 1; see also