<p>Compared to traditional therapist-assisted rehabilitation training, ankle rehabilitation robots (ARRs) can offer a wider variety of active and passive training strategies for stroke and fracture patients. This enhances patient recovery outcomes and efficiency while reducing physical exertion for therapists, thereby conserving rehabilitation medical resources. This paper first summarizes the current research status on the equivalent models of the human ankle, aiming to better reproduce its motion functions in the development of ARRs. Secondly, it systematically retrieves and screens literature on the configuration design of ARRs from databases including Web of Science, Engineering Village, and IEEE Xplore. Thirdly, from the perspective of configuration design, the existing ARRs are divided into five categories: based on classical parallel mechanisms, with spherical pair or universal joint limb, based on remote center-of-motion mechanisms, human–machine compatible types, and other types. Finally, the characteristics of each ARR category are summarized, the current challenges and future prospects faced by ARRs are highlighted, and the limitations of this paper are also discussed. This paper systematically reviews the research status of configuration design of ARRs, pointing out that shortcomings still exist in areas such as human–machine compatibility. Future efforts should further integrate the biomechanical characteristics of the ankle to deepen innovative design of human–machine compatible configurations.</p>