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This article discusses a new idea called cognitive radar. Three ingredients are basic to the constitution of cognitive radar: 1) intelligent signal processing, which builds on learning through interactions of the radar with the surrounding environment; 2) feedback from the receiver to the transmitter, which is a facilitator of intelligence; and 3) preservation of the information content of radar returns, which is realized by the Bayesian approach to target detection through tracking. All three of these ingredients feature in the echo-location system of a bat, which may be viewed as a physical realization (albeit in neurobiological terms) of cognitive radar. Radar is a remote-sensing system that is widely used for surveillance, tracking, and imaging applications, for both civilian and military needs. In this article, we focus on future possibilities of radar with particular emphasis on the issue of cognition. As an illustrative case study along the way, we consider the problem of radar surveillance applied to an ocean environment.