Models of braided-river deposition must be detailed, fully 3D, and preferably quantitative to be of use in understanding and predicting the nature of ancient deposits. In order to construct and validate adequate predictive models it is necessary to have information on: (1) variation and interaction of channel geometry, water flow and sediment transport in time and space in modern channel belts, as these control erosion and deposition, the formation and migration of channels and bars, and channel abandonment and filling; (2) 3D variation of bed geometry, texture, sedimentary structures and paleocurrents throughout modern channel-belt deposits, including the age and spatial arrangement of preserved parts of bars and channel fills; (3) long-term (more than hundreds of years) trends in channel and floodplain geometry, flow and sedimentary processes in order to understand channel-belt movements such as avulsions, and the spatial arrangement of channel-belt deposits relative to overbank deposits. Such information is rare because: (1) it is difficult to study modern braided-river geometry, flow and sedimentary processes throughout a range of the all-important high discharges; (2) detailed reconstructions of braided channel and bar geometry and movement are only available for the past half-century and cannot readily be linked to causative mechanisms; (3) 3D documentation of modern deposits below the water table (especially large scale features like lateral-accretion bedding) requires extensive coring and dating of the deposits, and geophysical profiling. As a result of this lack of information, and because of the quality of analysis and presentation of the information available, existing braided-river facies models are virtually useless as interpretive and predictive tools. The nature of the information available is critically reviewed. Using information from recent detailed field and laboratory studies of the geometry, flow and sedimentary processes in braided rivers of simple geometry, in single river bends, in channel confluences, and using some theoretical reasoning, it has been possible to construct fully 3D qualitative and quantitative models of braided river deposits. These models can be used to provide sophisticated quantitative interpretations of palaeochannel geometry, hydraulics and migration, as illustrated by comparison with some particularly well described examples of ancient braided river deposits.