<p>Non-imaging cusp concentrator (NICC) is an ideal concentrating collector that not merely collects direct solar radiation, but also captures a larger quantity of circumsolar radiation and diffuse radiation while offering the widest possible acceptance angle for a given concentration ratio. Depending on the required amount of solar radiation or fluid temperature, a non-imaging cusp concentrator can be combined with solar tracking. In this paper, the up-to-date technical research on non-imaging cusp concentrator is reviewed, and the concept, design principles and truncation theory of NICC are proposed. In addition, the technical characteristics of internal and external concentrating collectors are discussed, and the recent advancements of non-imaging cusp concentrator in the field of solar energy utilization such as photothermal utilization, photovoltaic utilization, seawater desalination and photocatalytic degradation are also summarized. Eventually, a comprehensive discussion was held on potential technical challenges that may arise during the future development of NICC, such as model fabrication, truncation design, solar tracking system integration, and widespread application. This research can be a reference for future scientific studies on NICC, which is of positive significance for the realization of peaking carbon dioxide emission.</p>