Surface digital elevation models (DEMs) and slope-related estimates of glacier thickness enable modelling of glacier-bed topographies over large ice-covered areas. Due to the erosive power of glaciers, such bed topographies can contain numerous overdeepenings, which when exposed following glacier retreat may fill with water and form new lakes. In this study, the bed overdeepenings for ~28000 glaciers (40775km²) of the Himalaya–Karakoram region are modelled using GlabTop2 (Glacier Bed Topography model version 2), in which ice thickness is inferred from surface slope by parameterizing basal shear stress as a function of elevation range for each glacier. The modelled ice thicknesses are uncertain (±30%), but spatial patterns of ice thickness and bed elevation primarily depend on surface slopes as derived from the DEM and, hence, are more robust. About 16000 overdeepenings larger than 10⁴ m² were detected in the modelled glacier beds, covering an area of ~2200 km² and having a volume of ~120 km³ (3–4% of present-day glacier volume). About 5000 of these overdeepenings (1800 km2) have a volume larger than 10⁶ m³. The results presented here are useful for anticipating landscape evolution and potential future lake formation with associated opportunities (tourism, hydropower) and risks (lake outbursts).