This paper reviews research done by the authors and their collaborators at IRI and beyond over the past decade on predictability and prediction of Indian summer monsoon rainfall (ISMR) on seasonal and sub-seasonal timescales. Empirical analyses of the daily ISMR characteristics at local scales pertinent to agriculture, based on IMD gridded data, reveal that the number of rainy days in the season is more predictable than the seasonal rainfall total; furthermore, this "weather-within-climate" predictability undergoes an important seasonal modulation and is highest in the early and late phases of the monsoon and lowest in the July-August core monsoon period. New research in calibrated multi-model seasonal forecasting of ISMR is presented based on the North American Multi-Model Ensemble and gridded IMD data, using the 2018 forecasts as a case study; these forecasts were issued in real-time in tercile-category probability format and were updated for the remainder of the 2018 monsoon season at the beginning of each calendar month from June to September. Sub-seasonal multimodel probabilistic predictions of ISMR in the weeks 2-3 range (8-21 day lead times) are constructed and analyzed, using the onset of the 2018 monsoon as an example; the hindcast skill of these week 2-3 gridded ISMR forecasts is shown to be substantial in the early and late stages of the monsoon season, consistent with the empirical findings from IMD data. Lastly, a hidden Markov model (HMM) of daily rainfall variability at a network of stations over monsoonal India is used to interpret the organized variation of rainfall across the multiple temporal scales that characterize ISMR.