Health care facility ventilation design greatly affects disease transmission by aerosols. The desire to control infection in hospitals and at the same time to reduce their carbon footprint motivates the use of unconventional solutions for building design and associated control measures. This paper considers indoor sources and types of infectious aerosols, and pathogen viability and infectivity behaviors in response to environmental conditions. Aerosol dispersion, heat and mass transfer, deposition in the respiratory tract, and infection mechanisms are discussed, with an emphasis on experimental and modeling approaches. Key building design parameters are described that include types of ventilation systems (mixing, displacement, natural and hybrid), air exchange rate, temperature and relative humidity, air flow distribution structure, occupancy, engineered disinfection of air (filtration and UV radiation), and architectural programming (source and activity management) for health care facilities. The paper describes major findings and suggests future research needs in methods for ventilation design of health care facilities to prevent airborne infection risk.