The Corbicula clams (Bivalvia: Cyrenidae) are an ecologically significant and widespread group of fresh- and brackish-water molluscs, playing a keystone role in aquatic ecosystems. Some species of this genus are subglobal invaders. The taxonomy of Corbicula remains very confusing, which hinders both fundamental and applied research on this genus. A comprehensive revision of the taxonomic structure of this group has been lacking so far. In this paper, we clarify the taxonomy, distribution, and evolutionary biogeography of the living representatives of the genus Corbicula, including species widely distributed in their non-native ranges, on the basis of the largest dataset of DNA sequences ever analysed. Our data reveal that the genus Corbicula contains two subgenus-level clades: Corbicula s.s. and Sphaerocorbicula Bolotov, Bespalaya & Aksenova subgen. nov. Our COI mtDNA and two-locus phylogenies reveal that the genus Corbicula contains not < 27 well-supported clusters corresponding to the species-level taxa. Two of them are described here as species new to science: Corbicula bilini Bespalaya, Kropotin, Kondakov, Konopleva & Bolotov sp. nov. (Bilin River, Myanmar) and C. lemroae Bespalaya, Kropotin, Kondakov, Konopleva & Bolotov sp. nov. (Lemro River, Myanmar). A new synonymy is established for five species of Corbicula and one is transferred from the family Sphaeriidae to Cyrenidae. Our fossil-calibrated phylogeny and generalised biogeographic model indicate that the most recent common ancestor of the genus Corbicula could have originated somewhere within a broad area covering Asia near the upper boundary of the Middle Cretaceous.