Heat pumps (HPs) have become pivotal for heating and cooling applications, serving as sustainable energy solutions. Coupled with renewable energy sources (RES) to run the compressor, which is the major energy-consuming component, they contribute to eco-conscious practices. Notably, their adaptability to be supplied by either alternating (AC) or direct (DC) currents, facilitated through converters, makes them more flexible for versatile renewable energy (RE) applications. This paper presents a comprehensive review of converter topologies employed in various HP applications. The review begins by exploring previous applied photovoltaic (PV)-HP projects, focusing on the gaps in the literature concerning the employed converter topologies. Additionally, the review extends to include a broader examination of the converter topologies that could be employed on the source and load sides of a system powered by a mix of renewable energy sources, such as photovoltaics (PV), wind turbines (WTs), and energy storage systems (ESS), and analyzes their strengths and weaknesses. Special emphasis is given to understanding the various topologies of the power electronics converters in the context of HP applications. Finally, the paper concludes with a summary of the literature gaps, challenges, and directions for future research.