The air source heat pump (ASHP) systems assisted by solar energy have drawn great attentions, owing to their great feasibility in buildings for space heating/cooling and hot water purposes. However, there are a variety of configurations, parameters and performance criteria of solar assisted ASHP systems, leading to a major inconsistency that increase the degree of complexity to compare and implement different systems. A comparative literature review is lacking, with the aim to evaluate the performance of various ASHP systems from three main solar sources, such as solar thermal (ST), photovoltaic (PV) and hybrid photovoltaic/thermal (PV/T). This paper thus conducts a systematic review of the prevailing solar assisted ASHP systems, including their boundary conditions, system configurations, performance indicators, research methodologies and system performance. The comparison result indicates that PV-ASHP system has the best techno-economic performance, which performs best in average with coefficient of performance (COP) of around 3.75, but with moderate cost and payback time. While ST-ASHP and PV/T-ASHP systems have lower performance with mean COP of 2.90 and 3.03, respectively. Moreover, PV/T-ASHP system has the highest cost and longest payback time, while ST-ASHP has the lowest ones. Future research are discussed from aspects of methodologies, system optimization and standard evaluation.