The coupled operation of solar energy and air source heat pump (ASHP) can effectively solve the intermittent problem of solar energy systems running alone and the problem of performance degradation of ASHP systems running alone in winter. The coupled system of solar energy and ASHP can be divided into direct expansion type and indirect expansion type according to the structure form, and the indirect expansion type can be divided into series type, parallel type, and hybrid type. Various architectural forms of the solar-air source heat pump coupled system (S–ASHP) have achieved enhanced energy efficiency by means of a series of strategies, including the optimization of collectors, the refinement of evaporator structures, and the regulation of the temperature within hot water storage tanks. Choosing the appropriate architecture needs to comprehensively consider factors such as the external environment and load demand. In this paper, a variety of S–ASHP are summarized in order to provide some guidance for the future application of S–ASHP systems in the field of heating.