This survey paper addresses the signal processing challenges for the design of radar-on-chip/in-package in the autonomous driving era, taking into account recent integration trends and technology capabilities. Radar signal processing platform specifications are discussed, and the radar sensor is compared to other competing sensors, such as Lidars and ultrasonics and video cameras, that aim at detecting still or moving objects too, and at measuring their motion parameters. This survey paper first focuses on signal processing techniques to be used for a cheap and powerefficient radar sensor, which operates in real-time while ensuring the automotive coverage-range needs. The main signal processing techniques for velocity-range estimation, direction estimation, waveform design and beamforming are analyzed, with particular emphasis on the radar physical layer co-design. Exploiting future evolution of embedded computing platforms, advanced signal processing techniques are enabled such as Multi-Input Multi-Output and cognitive radars, with adaptive waveforms to solve interference and spectrum scarcity issues.