The first global climatology of monsoon low-pressure systems is presented here, based on the ERA-Interim reanalysis. Low-pressure systems are classified into three intensity categories and particular focus is given to systems in the category corresponding to a traditional definition of monsoon depressions. Vortex tracks are identified using an automated algorithm applied to the distributions of 850 hPa relative vorticity, sea-level pressure and surface wind speed for 1979-2012. Roughly two to three times as many monsoon low-pressure systems form in the Northern Hemisphere as in the Southern Hemisphere during local summer. The frequency of genesis typically peaks in local summer, but low-pressure systems form throughout the year in every monsoon region. Interannual variability is weak, with standard deviations of summer counts typically being below 10{%} of the long-term summer mean. Regional composites reveal that monsoon depressions in India, the western Pacific and northern Australia share a common structure, consisting of a warm-over-cold core and a top-heavy column of potential vorticity that extends from the surface to the upper troposphere. A separate class of monsoon low-pressure systems develops over dry regions of West Africa and western Australia, with a shallow composite structure having a warm core in the lower troposphere and cyclonic potential vorticity confined to a thin near-surface layer. Low-pressure systems in nearly all monsoon regions are estimated to account for a large fraction, from about 40% to more than 80%, of summer precipitation on the poleward edge of the climatological mean precipitation maxima.