In order to improve walking efficiency, make walking gaits more natural and help robots realize complex motions, we introduce adaptable compliance to bipedal walking robots. Based on the review of the progress of bipedal walking robots with adaptable compliance, this paper presents the state-of-the-art research of both active and passive bipedal walking robots with adaptable compliance. For the four main problems in current studies, this paper predicts the tendency of bipedal walking robots with adaptable compliance, including applying compliant actuators in bipedal walking robots with adaptable compliance, study of compliance control methods, combination of bipedal robots and biological research, and applications of adaptable compliance in auxiliary walking devices such as prostheses and exoskeletons. This paper provides relevant theories, methods and technologies for obtaining bipedal walking robots with high efficiency, natural gaits and high versatility.