We review past, present and future North Atlantic hurricane activity based on analysis of observational records and models projections. When adjusted for likely missed tropical cyclones, the observational record does not show any significant increase or decrease of North Atlantic hurricane frequency. Downscaling results for most available CMIP5 models show a decrease or little change in overall frequency of tropical storms and hurricanes, although in the Atlantic basin, previous studies by other investigators report a wider range of change (+/-60%). Some model projections of late 21st century hurricane activity indicate an increase in frequency of the strongest storms (category 4-5 hurricanes). The projected increase is substantial (+100% per century) in the CMIP3 ensemble model downscaling, but much smaller (+40%) and only marginally significant in the CMIP5 ensemble model downscaling. Rainfall rates in the inner core of the hurricanes are projected to increase with potentially a substantial damage impact. The largest source of uncertainty in predicting changes in Atlantic tropical storms activity over the first half of the 21st century arises from the internal variability of the climate system. Nonetheless, some of these natural fluctuations appear to be predictable beyond seasonal time scale. We review recent predictability assessment results based on two CMIP5 models. Initializing these models with observational estimates leads to encouraging results in predicting multi-year variations in North Atlantic hurricane frequency. However the short record and the persistent character of the time series limits the ability to confidently predict North Atlantic hurricane activity for now. Remaining model biases, despite the tremendous improvement over the recent decades, and the changing observational system make it an ongoing challenge to simulate past hurricane activity and project or predict its future behavior.