This study examines the annual cycle of monsoon precipitation simulated by models from the Coupled Model Intercomparison Project phase 6 (CMIP6), focusing on model bias and future changes. Characteristics of the rainy season are quantified using a consistent method across the globe. Models exhibit rainy season onsets tens of days later than observed in some monsoon regions (India, Australia, and North America) and strong positive bias in summer rain rates in others (North America, West Africa, South America, and southern Africa). Projected next-century changes include lengthening of rainy seasons in the two largest Northern Hemisphere monsoon regions (South Asia and West Africa) and shortening in the two largest Southern Hemisphere regions (South America and southern Africa). Projected changes in the North American and Australian monsoons are less coherent across models. To understand these changes, the 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 shortening of the rainy season are spanned by an increasing equator-to-pole MSE gradient, suggesting their rainfall will be increasingly inhibited by ventilation by 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.