After more than one hundred years of statistical forecasting and fifty years of climate model development, this paper shows that the skill of predicting Indian monsoon rainfall with coupled atmosphere-ocean models initialized in May is statistically significant, and much higher than can be predicted empirically from May sea surface temperatures (SSTs). The superior skill of dynamical models is attributed to the fact that slowly evolving sea surface temperatures are the primary source of predictability, and to the fact that climate models produce more skillful predictions of June-September sea surface temperatures. The recent apparent breakdown in SST-monsoon relation can be simulated in coupled models, even though the relation is significant and relatively constant on an ensemble mean basis, suggesting that the observed breakdown could be due, in large part, to sampling variability. Despite the observed breakdown, skillful predictions of monsoon rainfall can be constructed using sea surface temperaturespredictedby dynamical models. This fact opens the possibility of using readily available seasonal predictions of sea surface temperatures to make real-time skillful predictions of Indian summer monsoon rainfall. In addition, predictors based on tendency of SST during spring information show skill during both the recent and historical periods and hence may provide more skillful predictions of monsoon rainfall than predictors based on a single month.