<p>Recompressed sCO₂ Brayton Cycles are topical in the narrative of sustainable energy conversion and are considered to be at 80 % technology readiness level, but still open to thermal efficiency (η_th) and levelized cost of energy enhancements. However, the lack of rigorous academic engagement in the specific nexus of concentrated solar plant Recompressed sCO₂ Brayton Cycles and Triply periodic minimal surface recuperators may be veiling the honey pot. This study surveys data over two decades around academic and research institutions on the history and trends of solar Recompressed sCO₂ Brayton Cycles and how recuperators contribute to their thermal and economic efficiency. Findings show that many theoretical studies on the Recompressed sCO₂ Brayton Cycles exist, but among concentrated solar plant Recompressed sCO₂ Brayton Cycles demonstration plants, there is a total of three (3) ongoing full scale testing stations in the United States, European Union and China and a couple others still in the construction and initial commissioning stage. The highest reported η_th is 54 % and the lowest levelized cost of energy is 0.059 $/kWh. Among the existing test stations worldwide, most use printed circuit heat exchanger recuperators, despite numerical studies presented in this study proving that Triply periodic minimal surface recuperators are more effectual on both thermal, hydraulic and levelized cost of energy performance. As a result, this study has made a strong case in proposing that better prospects may lie around Triply periodic minimal surface hybridization of recuperators retrofitted into concentrated solar plant Recompressed sCO₂ Brayton Cycles. The authors have strengthened their case by presenting literature evidence on the availability sCO₂ compatible alloys, maturity of Triply periodic minimal surface manufacturing technology, cost and time effectiveness of their fabrication.</p>