Automotive radars, along with other sensors such as lidar, (which stands for "light detection and ranging"), ultrasound, and cameras, form the backbone of self-driving cars and advanced driver assistant systems (ADASs). These technological advancements are enabled by extremely complex systems with a long signal processing path from radars/sensors to the controller. Automotive radar systems are responsible for the detection of objects and obstacles, their position, and speed relative to the vehicle. The development of signal processing techniques along with progress in the millimeter-wave (mm-wave) semiconductor technology plays a key role in automotive radar systems. Various signal processing techniques have been developed to provide better resolution and estimation performance in all measurement dimensions: range, azimuth-elevation angles, and velocity of the targets surrounding the vehicles. This article summarizes various aspects of automotive radar signal processing techniques, including waveform design, possible radar architectures, estimation algorithms, implementation complexity-resolution trade off, and adaptive processing for complex environments, as well as unique problems associated with automotive radars such as pedestrian detection. We believe that this review article will combine the several contributions scattered in the literature to serve as a primary starting point to new researchers and to give a bird's-eye view to the existing research community.