Solving stochastic optimization problems under partial observability, where one needs to adaptively make decisions with uncertain outcomes, is a fundamental but notoriously difficult challenge. In this talk, I will introduce a new concept called adaptive submodularity, which generalizes submodular set functions to adaptive policies. In many respects adaptive submodularity plays the same role for adaptive problems as submodularity plays for nonadaptive problems. Specifically, just as many nonadaptive problems with submodular objectives have efficient algorithms with good approximation guarantees, so too do adaptive problems with adaptive submodular objectives. We use this fact to recover and generalize several previous results in adaptive optimization, including results for active learning and adaptive variants of maximum coverage and set cover. Applications include machine diagnosis, observation selection and sensor placement problems, and adaptive viral marketing. Joint work with Andreas Krause.