Glaciers flowing over uneven bed topography or undergoing extensional flow develop tensile stresses, and where these exceed the fracture strength of ice, crevasses open. Their distribution expresses the surface strain-rate field and enhances local ablation. Yet observations of where crevasses occur across Alpine glaciers remain scarce, and the theoretical controls on their formation, established largely from individual glaciers, are untested across a diverse glacier population. Here we present the first country-scale inventory of visible crevasses, mapped across all Austrian glaciers from high-resolution remote-sensing imagery, and analyse their spatial distribution and structural controls across six mountain regions. Crevasse density varies strongly between regions, peaking on the steep glaciers of the Zillertal Alps and the fast-flowing glaciers of the High Tauern, and reaching its lowest values on the large, low-gradient glaciers of the Ötztal and Stubai Alps. Linking crevasses to surface topography and ice dynamics, we show that crevassing is favoured by convex surfaces, steep slopes, and along-flow changes in slope. Ice-flow velocity and driving stress instead behave as thresholds, distinguishing highly crevassed terrain only once exceeded. We find no relationship with along-flow velocity change, despite longitudinal extension being the classical mechanism, indicating that much of the regional crevasse signal is inherited rather than locally generated and raising questions of advection and suppressed crevasse healing under reduced overburden pressure. The inventory supports route planning in published hiking maps and provides an observational basis for representing crevasse-enhanced heat exchange in mass-balance models and calibrating damage-mechanics schemes in ice-flow models.