The last forty years of the digital revolution has been driven by one simple fact: the number of transistors on a silicon chip doubles every couple of years. Today we are witnessing a second form of exponential growth: in the quantity of data being collected and stored. It is driving a transformation in information technology, from solutions that are explicitly hand-crafted to those which are learned from data. Real-world data, however, is full of complexity, ambiguity and uncertainty and so the data revolution is driving a corresponding transformation from computing with logic to computing with probabilities. This talk will introduce the key ideas of computing with uncertainty, and will be illustrated with tutorial examples and real-world case studies.