How might we architect interactive systems that have better models of the tasks we're trying to perform, learn over time, help refine ambiguous user intents, and scale to large or repetitive workloads? In this talk I will present Predictive Interaction, a framework for interactive systems that shifts some of the burden of specification from users to algorithms, while preserving human guidance and expressive power. The central idea is to imbue software with domain-specific models of user tasks, which in turn power predictive methods to suggest a variety of possible actions. I will illustrate these concepts with examples drawn from widely-deployed systems for data transformation and visualization (with reported order-of-magnitude productivity gains) and then discuss associated design considerations and future research directions.