The drying needs of agricultural, industrial process heat requirements and for space heating, solar energy is one of the prime sources which is renewable and pollution free. As the solar energy is inconsistent and nature dependent, more often there is a mismatch between the solar thermal energy availability and requirement. This drawback could be addressed to an extent with the help of thermal energy storage systems combined with solar air heaters. This review article focuses on solar air heaters with integrated and separate thermal energy storage systems as well as greenhouses with thermal storage units. A comprehensive study was carried out in solar thermal storage units consisting of sensible heat storage materials and latent heat storage materials. As the phase change heat storage materials offer many advantages over the sensible heat storage materials, the researchers are more interested in this system. The charging and discharging characteristics of thermal storage materials with various operational parameters have been reported. All the possible solar air heater applications with storage units have also been discussed.