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We survey the current state of millimeter-wave (mmWave) radar applications in robotics with a focus on unique capabilities, and discuss future opportunities based on the state of the art. Frequency modulated continuous wave mmWave radars operating in the 76–81 GHz range are an appealing alternative to lidars, cameras, and other sensors operating in the near-visual spectrum. Radar has been made more widely available in new packaging classes, more convenient for robotics and its longer wavelengths have the ability to bypass visual clutter, such as fog, dust, and smoke. We begin by covering radar principles as they relate to robotics. We then review the relevant new research across a broad spectrum of robotics applications beginning with motion estimation, localization, and mapping. We then cover object detection and classification, and then close with an analysis of current datasets and calibration techniques that provide entry points into radar research.