This study examines the annual cycle of monsoon precipitation simulated by models from the Coupled Model Intercomparison Project phase 6 (CMIP6), then uses moist energy diagnostics to explain globally inhomogeneous projected future changes. Rainy season characteristics are quantified using a consistent method across the globe. Model bias is shown to include rainy season onsets tens of days later than observed in some monsoon regions (India, Australia, and North America) and overly large summer precipitation in others (North America, South America, and southern Africa). Projected next-century changes include rainy season lengthening in the two largest Northern Hemisphere monsoon regions (South Asia and central Sahel) and shortening in the two largest Southern Hemisphere regions (South America and southern Africa). Changes in the North American and Australian monsoons are less coherent across models. To understand these changes, relative moist static energy (MSE) is defined as the difference between local and tropical-mean surface air MSE. Future changes in relative MSE in each region correlate well with onset and demise date changes. Furthermore, Southern Hemisphere regions projected to undergo rainy season shortening are spanned by an increasing equator-to-pole MSE gradient, suggesting their rainfall will be increasingly inhibited by fluxes of dry extratropical air; Northern Hemisphere regions with projected lengthening of rainy seasons undergo little change in equator-to-pole MSE gradient. Thus, although model biases raise questions on the reliability of some projections, these results suggest that globally inhomogeneous future changes in monsoon timing may be understood through simple measures of surface air MSE.