Most studies related to concrete made with recycled aggregates (RA) use uncontaminated aggregates produced in the laboratory, revealing the potential to re-use as much as 100%. However, industrially produced RA contain a certain level of impurities that can be deleterious for Portland cement concrete, thus making it difficult for the concrete industry to use such investigations unless uncontaminated RA are used. This chapter reviews current knowledge on concrete made with RA, with a focus on the crucial importance of the presence of impurities, and how those aggregates are not suitable for the production of high-performance concrete (HPC). The potential of geopolymers to produce HPC based on high volume RA is also discussed.