Binary fish passage models are considered by many fisheries' managers to be the best available practice for culvert inventory assessments and for fishway design. Misunderstandings between different passage-modelling approaches often arise, however, because of the absence of a formal comparison between the different approaches that include detailed derivations with consistent terminology and example applications. In this paper, one-dimensional binary fish passage models were reviewed, and derivations from basic principles were provided for clarification. For uniform flow, a simple exhaustion-threshold (ET) model equation was derived that predicts the flow velocity threshold in a fishway that causes exhaustion at a given maximum distance of ascent if a fish swims at the optimal ground speed. Velocities at or above the threshold predict failure to pass (exclusion). Velocities below the threshold predict passage. The ET model was therefore intuitive and easily applied to predict passage or exclusion. It was also shown to be consistent with the ascent-distance (AD) model that shows that fish must adopt an optimal ground speed to maximize AD. The limitation of passage models to uniform flow was addressed by deriving a general model framework for passage that accounts for nonuniform flow conditions more commonly found in the field, including backwater and drawdown water-surface profiles. Comparison of these models with experimental observations of volitional passage for top-performing western mosquitofish Gambusia affinis indicates reasonable prediction of binary outcomes (passage or exclusion) if the flow velocity is not near the threshold flow velocity. More research is needed on fish behaviour, passage strategies under nonuniform flow regimes and stochastic methods that account for individual differences in swimming performance. Future experiments should track and measure ground speeds of ascending fish to test passage strategies and to improve model predictions. Stochastic models, such as Monte-Carlo techniques, that account for different passage performance among individuals and allow prediction of the percentage of fish passing are needed to improve fish passage prediction. Published in 2011 by John Wiley & Sons, Ltd.