Automotive radars sense the traffic environment using electromagnetic wave. It is of low cost and works under all weather conditions throughout the day, so is of great importance for intelligent traffic and autonomous driving. Nowadays, researchers in this field focus on high-accuracy sensing of range and velocity, high resolution angle estimation and high performance multiple extended target tracking. In this paper, the existing methods in waveform design, antenna design, angle estimation and target tracking algorithms for automotive radar are reviewed. The recent literatures on radar anti-jamming, MIMO coding and extended target state estimation are summarized, aiming to provide an introduction and directions for future research.