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Cognitive sensing refers to a reconfigurable sensor that dynamically adapts its sensing mechanism by using stochastic control to optimize its sensing resources. For example, cognitive radars are sophisticated dynamical systems; they use stochastic control to sense the environment, learn from it relevant information about the target and background, then adapt the radar sensor to satisfy the needs of their mission. The last two decades have witnessed intense research in cognitive/adaptive radars.This paper discusses addresses the next logical step, namely inverse cognitive sensing. By observing the emissions of a sensor (e.g. radar or in general a controlled stochastic dynamical system) in real time, how can we detect if the sensor is cognitive (rational utility maximizer) and how can we predict its future actions? The scientific challenges involve extending Bayesian filtering, inverse reinforcement learning and stochastic optimization of dynamical systems to a data-driven adversarial setting. Our methodology transcends classical statistical signal processing (sensing and estimation/detection theory) to address the deeper issue of how to infer strategy from sensing. The generative models, adversarial inference algorithms and associated mathematical analysis will lead to advances in understanding how sophisticated adaptive sensors such as cognitive radars operate.