Radar, as one of the sensors for human activity recognition (HAR), has unique characteristics such as privacy protection and contactless sensing. Radar-based HAR has been applied in many fields such as human–computer interaction, smart surveillance and health assessment. Conventional machine learning approaches rely on heuristic hand-crafted feature extraction, and their generalization capability is limited. Additionally, extracting features manually is time–consuming and inefficient. Deep learning acts as a hierarchical approach to learn high-level features automatically and has achieved superior performance for HAR. This paper surveys deep learning based HAR in radar from three aspects: deep learning techniques, radar systems, and deep learning for radar-based HAR. Especially, we elaborate deep learning approaches designed for activity recognition in radar according to the dimension of radar returns (i.e., 1D, 2D and 3D echoes). Due to the difference of echo forms, corresponding deep learning approaches are different to fully exploit motion information. Experimental results have demonstrated the feasibility of applying deep learning for radar-based HAR in 1D, 2D and 3D echoes. Finally, we address some current research considerations and future opportunities.