The main objective of this research is to use recycled concrete fines (RCFs) in cement blends. RCF is the fraction of the Construction and Demolition Waste (CDW) with a size smaller than 0.15 mm. Currently, RCFs usually go to landfills because of their low hydration reactivity and the high water demand of the corresponding mortars and concretes. Because of these two reasons, this waste cannot be used to replace a significant fraction of PC. However, the carbonation of RCFs (cRCFs) produced a chemical fixation of CO2 which diminished the water demand and enhanced the reactivity of the resulting PC-cRCFs blends by the pozzolanic reaction. Therefore, the advantages are: (I) it valorises one waste, i.e. RCF; (II) it utilises CO2, contributing to decreasing emissions and developing the CO2-economy; and (III) it reduces the need for PC, which is very intensive in CO2 emissions, producing low-carbon cements. The overall CO2 footprints of the resulting concretes could approach zero.