Compliance control is highly relevant to human safety in human–robot interaction (HRI). This paper presents a review of various compliance control techniques. The paper is aimed to provide a good background knowledge for new researchers and highlight the current hot issues in compliance control research. Active compliance, passive compliance, adaptive and reinforcement learning-based compliance control techniques are discussed. This paper provides a comprehensive literature survey of compliance control keeping in view physical human robot interaction (pHRI) e.g., passing an object, such as a cup, between a human and a robot. Compliance control may eventually provide an immediate and effective layer of safety by avoiding pushing, pulling or clamping in pHRI. Emerging areas such as soft robotics, which exploit the deformability of biomaterial as well as hybrid approaches which combine active and passive compliance are also highlighted.