The transition toward sustainable infrastructure in the construction sector necessitates the practical integration of Circular Economy (CE) principles, particularly through the valorization of recycled materials in concrete applications. This review critically synthesizes recent advancements in the use of recycled polyethylene terephthalate (PET), glass powder, and crumb rubber as partial replacements for conventional aggregates in Ordinary Portland Cement (OPC)-based concrete. The incorporation of these secondary materials has demonstrated the ability to reduce the environmental footprint of concrete production—achieving up to 25% reductions in greenhouse gas emissions and diverting significant volumes of waste from landfills—while maintaining structural viability with compressive strength retention levels exceeding 90% in several optimized mix designs. Enhanced ductility, thermal resistance, and reduced density further support their application in specialized construction scenarios. Beyond material characterization, the review systematically examines implementation enablers, including regulatory alignment, life-cycle-based procurement, and design-for-deconstruction strategies. It also highlights critical gaps such as the absence of harmonized standards, variability in recycled material quality, and systemic barriers to market uptake. Addressing these challenges is essential for scaling CE integration and achieving measurable sustainability gains across the built environment. This study aims to inform policy, practice, and research trajectories by linking material innovation with operational frameworks that support regenerative construction systems.