Practices that reuse concrete pieces in new building or infrastructure projects are currently diversifying as concrete reuse gains more and more relevance for sustainability. The present research provides a yet missing identification of the main approaches to these practices and introduces a new set of criteria to compare them. Five types of sourced concrete pieces are identified, three resulting from careful deconstruction and two from demolition. The study shows that approaches allowing the best re-utilization rate of the structural capacities of the concrete pieces are less compatible with current demolition practices, in contrast to approaches reusing debris. The reuse of wall and slab panels, beams, and columns is a promising approach as it implies a low to medium level of constraints on the new design while recovering the capabilities of discarded reinforced concrete equivalently. A few dozen built precedents have already applied this approach to precast components, but applications reusing cast-in-place concrete are lacking, despite considerable CO2 emissions reduction.