Background: The order Dasyuromorphia is a diverse radiation of faunivorous marsupials, comprising >80 modern species in Australia and New Guinea. It includes dasyurids, the numbat (the myrmecobiid Myrmecobius fasciatus) and the recently extinct thylacine (the thylacinid Thylacinus cyncocephalus). There is also a diverse fossil record of dasyuromorphians and "dasyuromorphian-like" taxa known from Australia. We present the first total evidence phylogenetic analyses of the order, based on combined morphological and molecular data (including a novel set of 115 postcranial characters), to resolve relationships and calculate divergence dates. We use this information to analyse the diversification dynamics of modern dasyuromorphians. Results: Our morphology-only analyses are poorly resolved, but our molecular and total evidence analyses confidently resolve most relationships within the order, and are strongly congruent with recent molecular studies. Thylacinidae is the first family to diverge within the order, and there is strong support for four tribes within Dasyuridae (Dasyurini, Phascogalini, Planigalini and Sminthopsini). Among fossil taxa, Ankotarinja and Keeuna do not appear to be members of Dasyuromorphia, whilst Barinya and Mutpuracinus are of uncertain relationships within the order. Divergence dates calculated using total evidence tip-And-node dating are younger than both molecular node-dating and total evidence tip-dating, but appear more congruent with the fossil record and are relatively insensitive to calibration strategy. The tip-And-node divergence dates indicate that Dasyurini, Phascogalini and Sminthopsini began to radiate almost simultaneously during the middle-To-late Miocene (11.5-13.1 MYA; composite 95% HPD: 9.5-15.9 MYA); the median estimates for these divergences are shortly after a drop in global temperatures (the middle Miocene Climatic Transition), and coincide with a faunal turnover event in the mammalian fossil record of Australia. Planigalini radiated much later, during the latest Miocene to earliest Pliocene (6.5 MYA; composite 95% HPD: 4.4-8.9 MYA); the median estimates for these divergences coincide with an increase in grass pollen in the Australian palynological record that suggests the development of more open habitats, which are preferred by modern planigale species. Conclusions: Our results provide a phylogenetic and temporal framework for interpreting the evolution of modern and fossil dasyuromorphians, but future progress will require a much improved fossil record.