Hundreds of thousands of individuals experience traumatic injuries each year. Some are mild to moderate in nature and patients experience full functional recovery and little change to their physical appearance. Others result in enduring, if not permanent, changes in physical functioning and appearance. Reconstructive plastic surgical procedures are viable treatments options for many patients who have experienced the spectrum of traumatic injuries. The goal of these procedures is to restore physical functioning and reduce the psychosocial burden of living with an appearance that may be viewed negatively by the patient or by others. Even after receipt of reconstructive procedures, many patients are left with residual disfigurement. In some, disability and disfigurement may be so profound that individuals are candidates for vascularized composite allotransplantation (VCA) procedures, i.e., the transplantation of a vascularized human body part containing multiple tissue types (skin, muscle, bone, nerves, and blood vessels) as an anatomical and/or structural unit. This narrative review paper summarizes the literature on the psychosocial burden experienced by those who have visible disfigurement. While many of these individuals experience stigma and discrimination, relatively few studies have employed a stigma framework to understand the psychosocial sequelea. This paper briefly addresses this framework. Last, particular focus is given to the psychosocial issues of individuals with particularly severe injuries who are potential candidates for VCA procedures.