Optical coherence tomography (OCT) is an interferometric technique for micron-level imaging in biological and non-biological contexts. As a non-invasive, non-ionizing, and video-rate imaging modality, OCT is widely used in biomedical and clinical applications, especially ophthalmology, where it functions in many roles, including tissue mapping, disease diagnosis, and intrasurgical visualization. In recent years, the rapid growth of medical robotics has led to new applications for OCT, primarily for 3D free-space scanning, volumetric perception, and novel optical designs for specialized medical applications. This review paper surveys these recent developments at the intersection of OCT and robotics and organizes them by degree of integration and application, with a focus on biomedical and clinical topics. We conclude with perspectives on how these recent innovations may lead to further advances in imaging and medical technology.