Nuclear and radiological accidents are not frequent but may lead to major consequences in the population. For the health systems, the need to handle a large number of victims will probably remain as an exception. However, a high number of affected victims can be expected in some terrorist scenarios. In addition, medical accidents in radiotherapy, fluoroscopy and diagnostic radiology have increased the number of patients with severe radiation injuries considerably, especially in developed countries. Given the increased use of ionising radiation for industrial and medical purposes and new technological applications emerging, the number of accidents may increase in the future. Consequently, the early identification and adequate management of these emergencies is a priority, as well as the need for medical preparedness, requiring knowledge about various emergency scenarios and planning appropriate responses to them before they occur. Unfortunately, medical professionals have a substantial knowledge gap in identifying and treating injured persons affected by ionising radiation. As managing radiation accidents is a very challenging process, exercises must be carried out to organise a well-trained multidisciplinary group of professionals to manage any radiation accident properly. Efforts on a continuously updated guidance system should be developed. In addition, new approaches to foster sustainable interdisciplinary and international cooperative networks on radiation injuries are necessary. Lessons learned from past nuclear and radiological emergencies have significantly contributed to strengthening scientific knowledge and increasing the available medical information on the effects of ionising radiation in the human body. In this context, radiation emergency medicine has emerged as a discipline that contributes to the diagnosis, treatment, medical follow-up and prognosis of persons affected by radiation injuries in a nuclear or a radiological emergency. In this paper, we review some relevant concepts related to the medical preparedness and multidisciplinary response required to attend to persons affected by these emergencies.