AI seems to be making rapid advances in many domains. With enough data and the right algorithms, does everything become predictable? What would this mean for healthcare? Similar questions are being asked in many fields. I teamed up with Matt Salganik to survey the limits to prediction in a dozen domains ranging from computer vision to civil wars. Based on our analysis, I will present a set of heuristics to identify the types of problems where we can expect to see genuine and continuing improvements, versus the problems where there are strong limits to prediction and commercial claims of breakthroughs tend to be snake oil. I will apply these heuristics to several problems in healthcare.