With about 5000 species in ca. 180 genera, the Muscidae is the most species-rich family in the muscoid grade of Calyptratae (Diptera: Cyclorrhapha), the others being the Fanniidae, Scathophagidae and Anthomyiidae. Muscidae is remarkable for its young age, high species diversity in all biogeographic regions, and an unusually diverse range of feeding habits at the larval stage (e.g., saprophagy, phytophagy, carnivory, endoparasitism, haematophagy). We here review muscid classification and biology and present a molecular phylogeny based on four mitochondrial genes (12S, 16S, COI, CYTB) and three nuclear genes (28S, Ef1a, and CAD) for 84 species from 40 genera. Our analysis is the first to include species from all biogeographic regions and all currently recognised muscid subfamilies and tribes. We provide strong support for the monophyly of the Muscidae, and for the first time also for the first split within this family. The ancestral larval feeding habit is reconstructed to be saprophagy with more specialised coprophagous saprophagy, phytophagy, and carnivory evolving multiple times from saprophagous ancestors. The origins of carnivory in larvae are significantly correlated with a reduction of the number of larval instars from three (ancestral) to two and one. The genus Achanthiptera which was previously in its own subfamily is shown to be closely related to Azeliini. However, it appears that Azeliinae is paraphyletic because Muscinae is sister-group to the Azeliini while the azeliine Reinwardtiini are polyphyletic. Coenosiinae and Muscinae are monophyletic, but Muscini is paraphyletic with regard to Stomoxyini. Because many subfamilies are apparently para- or even polyphyletic, we review the history of muscid classification in order to reveal how the currently used classification originated.