Three new genera are described, providing valuable new information on the phylogeny and biogeography of the family Dermestidae: Derbyana, gen. nov., containing only D. matthewsi, sp. nov. from north-western Australia; Orphilodes, gen. nov., with three Australian species, O. australis, sp. nov. (type of the genus), O. minor, sp. nov. and O. malleecola, sp. nov.; and Trichodryas, gen. nov., with one described species, T. esoterica sp. nov., from the Malay Peninsula and undescribed species from the Sulu Archipelago, Sabah, Kalimantan and Java. A cladistic analysis is included based on a matrix consisting of the three new genera, exemplar genera representing all major groups of Dermestidae and outgroup exemplars from the families Eucinetidae, Derodontidae, Nosodendridae, Endecatomidae and Bostrichidae. Based on the results, a new supergeneric classification is proposed and compared with those in other recent works on Dermestidae and related groups. Recognised subfamilies and tribes include Orphilinae, Attageninnae, Thorictinae, Dermestinae (Marioutini and Dermestini), Megatominae and Trinodinae (Thylodriini and Trinodini). Trichelodini is suppressed and Hexanodes Blair is removed from synonymy with Trichelodes Carter. Keys are given to adults and larvae of the subfamilies of Dermestidae and the genera of Orphilinae, Dermestinae and Trinodinae.