Many clinical procedures would benefit from direct and intuitive real-time visualization of anatomy, surgical plans, or other information crucial to the procedure. Three-dimensional augmented reality (3D-AR) is an emerging technology that has the potential to assist physicians with spatial reasoning during clinical interventions. The most intriguing applications of 3D-AR involve visualizations of anatomy or surgical plans that appear directly on the patient. However, commercially available 3D-AR devices have spatial localization errors that are too large for many clinical procedures. For this reason, a variety of approaches for improving 3D-AR registration accuracy have been explored. The focus of this review is on the methods, accuracy, and clinical applications of registering 3D-AR devices with the clinical environment. The works cited represent a variety of approaches for registering holograms to patients, including manual registration, computer vision-based registration, and registrations that incorporate external tracking systems. Evaluations of user accuracy when performing clinically relevant tasks suggest that accuracies of approximately 2 mm are feasible. 3D-AR device limitations due to the vergence-accommodation conflict or other factors attributable to the headset hardware add on the order of 1.5 mm of error compared to conventional guidance. Continued improvements to 3D-AR hardware will decrease these sources of error.