Radar automatic target recognition (RATR) technology is fundamental but complicated system engineering that combines sensor, target, environment, and signal processing technology, etc. It plays a significant role in improving the level and capabilities of military and civilian automation. Although RATR has been successfully applied in some aspects, the complete theoretical system has not been established. At present, deep learning algorithms have received a lot of attention and have emerged as potential and feasible solutions in RATR. This paper mainly reviews related articles published between 2010 and 2022, which corresponds to the period when deep learning methods were introduced into RATR research. In this paper, the current research status of radar target characteristics is summarized, including motion, micro-motion, one-dimensional, and two-dimensional characteristics, etc. This paper reviews the progress of deep learning methods in the feature extraction and recognition of radar target characteristics in recent years, including space, air, ground, sea-surface targets, etc. Due to more and more attention and research results published in the past few years, it is hoped that this review can provide potential guidance for future research and application of deep learning in fields related to RATR.