An overview of advances in the observation, modelling, forecasting, and understanding of flows through gaps achieved in the Mesoscale Alpine Programme is given. Gaps are lateral constrictions of topography (level gaps) often combined with vertical terrain changes (passes). Of the possible flow configurations, only an asymmetric one (relatively deep and slow upstream, accelerating and thinning downstream), which connects two different ‘reservoirs’ on each side of the gap, is examined. The flow is strongly nonlinear, making hydraulics (reduced-gravity shallow-water theory) rather than linear theory the simplest conceptual model to describe gap flow. Results from idealized topographical and flow conditions are presented, together with gap flows through a pass in the central Alpine Wipp Valley. For a given depth of the upstream reservoir, the gap controls the mass flux through it and marks the transition from a subcritical flow state upstream to a supercritical one downstream, which eventually adjusts to the downstream ‘reservoir’ in a hydraulic jump. Three gap flow prototypes were found: a classical layer one with neutral stratification and a capping inversion and two with a continuous stratification, for which a special analytical self-similar hydraulic solution exists. In all three cases, a deepening wedge of nearly mixed and stagnant air forms on top of the gap flow plunging down from the pass. The descent causes a warming and (relative) drying of the air, making gap flows a special case of föhn. Topographical variations smaller than the gap scale cause additional hydraulic jumps, flow separation, vorticity banners, gravity waves, and interactions with cold pools. Turbulent friction cannot be neglected. The climatological frequency of gap flows depends on the establishment of two different reservoirs and reaches 20% for the Wipp Valley. Copyright © 2007 Royal Meteorological Society