As computer vision algorithms are becoming more capable, their applications in clinical systems will become more pervasive. These applications include diagnostics such as colonoscopy and bronchoscopy, guiding biopsies and minimally invasive interventions and surgery, automating instrument motion and providing image guidance using pre-operative scans. Many of these applications depend on the specific visual nature of medical scenes and require designing and applying algorithms to perform in this environment. In this review, we provide an update to the field of camera-based tracking and scene mapping in surgery and diagnostics in medical computer vision. We begin with describing our review process, which results in a final list of 515 papers that we cover. We then give a high-level summary of the state of the art and provide relevant background for those who need tracking and mapping for their clinical applications. We then review datasets provided in the field and the clinical needs therein. Then, we delve in depth into the algorithmic side, and summarize recent developments, which should be especially useful for algorithm designers and to those looking to understand the capability of off-the-shelf methods. We focus on algorithms for deformable environments while also reviewing the essential building blocks in rigid tracking and mapping since there is a large amount of crossover in methods. Finally, we discuss the current state of the tracking and mapping methods along with needs for future algorithms, needs for quantification, and the viability of clinical applications in the field. We conclude that new methods need to be designed or combined to support clinical applications in deformable environments, and more focus needs to be put into collecting datasets for training and evaluation.