Climate change can affect the indoor environment due to heat and mass transfers between indoor and outdoor environments. To mitigate climate change impacts and adapt buildings to the changing environment, changes in building characteristics and occupants’ behavior may occur. To characterize the effects of climate change on indoor air quality (IAQ), the present review focused on four aspects: (1) experimental and modeling studies that relate IAQ to future environmental conditions, (2) evolution of indoor and outdoor air concentrations in the coming years with regard to temperature rise, (3) climate change mitigation and adaptation actions in the building sector, and (4) evolution of human behavior in the context of climate change. In the indoor environment, experimental and modeling studies on indoor air pollutants highlighted a combined effect of temperature and relative humidity on pollutant emissions from indoor sources. Five IAQ models developed for future climate data were identified in the literature. In the outdoor environment, the increasing ambient temperature may lead directly or indirectly to changes in ozone, particle, nitrogen oxides, and volatile organic compound concentrations in some regions of the world depending on the assumptions made about temperature evolution, anthropogenic emissions, and regional regulation. Infiltration into buildings of outdoor air pollutants is governed by many factors, including temperature difference between indoors and outdoors, and might increase in the years to come during summer and decrease during other seasons. On the other hand, building codes in some countries require a higher airtightness for new and retrofitted buildings. The building adaptation actions include the reinforcement of insulation, implementation of new materials and smart building technologies, and a more systematic and possibly longer use of air conditioning systems in summer compared to nowadays. Moreover, warmer winters, springs, and autumns may induce an increasing duration of open windows in these seasons, while the use of air conditioning in summer may reduce the duration of open windows.