This chapter provides an overview of the theory of controlled sensing, and its application to the sequential design of data-acquisition and decision-making processes. Based on the theory, it provides an overview of the applications to the quickest detection and localization of anomalies in power systems. This application is motivated by the fact that agile localization of anomalous events plays a pivotal role in enhancing the overall reliability of the grid and avoiding cascading failures. This is especially of paramount significance in the large-scale grids due to their geographical expansions and the large volume of data generated. Built on the theory of controlled sensing, the chapter discusses a stochastic graphical framework for localizing the anomalies with the minimum amount of data. This framework capitalizes on the strong correlation structures observed among the measurements collected from different buses. This framework, at its core, collects the measurements sequentially and progressively updates its decision about the location of the anomaly.