The taxonomic distribution and evolution of viviparity in Diptera is critically reviewed. The phenomenon ranges from ovoviviparity (eggs deposited at an advanced stage of embryonic development; larva emerges immediately after deposition), through viviparity (larva hatches inside female before deposition) to pupiparity (offspring deposited as pupa). Some Diptera are known to be facultatively viviparous, which is hypothesized to be a step towards the evolution of obligate viviparity. Obligate viviparity is found to comprise unilarviparity (single large larva in maternal uterus) which evolved many times independently, the rare oligolarviparity (more than one but not more than 12 larvae) and multilarviparity (large numbers of developing eggs or larvae in uterus) which is typical for the two largest clades of viviparous Diptera. Unilarviparity is either lecithotrophic (developing larva nourished by yolk of egg) or pseudo-placental (larva nourished by glandular secretions of mother). Viviparity has clearly evolved on many separate occasions in Diptera. It is recorded in 22 families, and this review identifies at least 61 independent origins of viviparity. Six families appear to have viviparity in their ground-plan. Some families have a single evolution of viviparity, others multiple evolutions. Guimaraes' model for the evolution of viviparity in Diptera is tested against phylogenetic information and the adaptive significance of viviparity is reviewed in detail. Possible correlations with life-history parameters (coprophily, parasitism, breeding in ephemeral plant parts, malacophagy and adult feeding habits – especially haematophagy) are analysed critically, as are potential advantages (shorter larval life, less investment in yolk by mother, protection of vulnerable stages, better access to breeding substrates, predation on competitors). Morphological constraints, adaptations and exaptations are reviewed, including the provision of an incubation space for the egg(s), the positioning of the egg(s) in the uterus, and maternal glands. The main morphological adaptations include greater egg size, reduction of egg respiratory filaments, thinning of chorion, modified larval respiratory system and mouthparts, and instar skipping. Female morphology and behaviour is particularly strongly modified for viviparity. The terminalia are shortened, the vagina is more muscular and tracheated, and the ovaries of unilarviparous species have a reduced number of ovarioles with alternate ovulation. Many of the final conclusions are tentative, and a plea is made for more detailed morphological and experimental study of many of the viviparous species. Viviparity in Diptera provides a fascinating example of multiple parallel evolution, and a fertile field for future research.