The amount of electrical energy produced by a given solar photovoltaic module can be increased by using concentrated solar radiation. The task can be accomplished by integrating optical concentrators with flat PV modules. Compound parabolic concentrators (CPCs) have emerged as one of the best options for concentrating PV applications due to their ability to collect both direct and diffuse solar radiation and being suitable for stationary installation. Over the last few decades, various designs of CPCs have been proposed and investigated by many researchers for concentrating PV applications. This article presents a comprehensive review of recent developments in CPC designs and applications for PV systems. This work mainly focuses on identifying the major challenges and research opportunities related to the design and development of CPCs, rendering them more beneficial for solar energy conversion. It has been found that although the outputs of CPC-based PV systems are superior to their counterparts without CPCs, some challenges still exist that need to be addressed to enable the commercialization of CPC-based solar systems. The primary sources of energy losses in CPCs include imperfections in the reflecting surfaces, non-uniform solar flux distribution on the receiver surface, solar cell series resistance, increased solar cell temperature due to solar radiation concentration, and relatively low concentration ratios achievable by CPCs. Finally, future recommendations have been outlined, highlighting the potential research opportunities and challenges being faced by prospective researchers working in the field of low concentrating solar PV systems. © 2022 The Authors