Today’s mobile phones are far from the mere communication devices they were 10 years ago. Equipped with sophisticated sensors and advanced computing hardware, phones can be used to infer users’ location, activity, social setting, and more. As devices become increasingly intelligent, their capabilities evolve beyond inferring context to predicting it, and then reasoning and acting upon the predicted context. This article provides an overview of the current state of the art in mobile sensing and context prediction paving the way for full-fledged anticipatory mobile computing. We present a survey of phenomena that mobile phones can infer and predict, and offer a description of machine learning techniques used for such predictions. We then discuss proactive decision making and decision delivery via the user-device feedback loop. Finally, we discuss the challenges and opportunities of anticipatory mobile computing.