The burden of HIV/AIDS and other transmissible diseases is higher in prison and jail settings than in the non-incarcerated communities that surround them. In this comprehensive review, we discuss available literature on the topic of clinical management of people infected with HIV, hepatitis B and C viruses, and tuberculosis in incarcerated settings in addition to co-occurrence of one or more of these infections. Methods such as screening practices and provision of treatment during detainment periods are reviewed to identify the effect of community-based treatment when returning inmates into the general population. Where data are available, we describe differences in the provision of medical care in the prison and jail settings of low-income and middle-income countries compared with high-income countries. Structural barriers impede the optimal delivery of clinical care for prisoners, and substance use, mental illness, and infectious disease further complicate the delivery of care. For prison health care to reach the standards of community-based health care, political will and financial investment are required from governmental, medical, and humanitarian organisations worldwide. In this review, we highlight challenges, gaps in knowledge, and priorities for future research to improve health-care in institutions for prisoners.