Copper-based　catalysts　for　the　hydrogenation　of　CO2　to　methanol　have　attracted　much　interest.　The　complex　nature　of　these　catalysts,　however,　renders　the　elucidation　of　their　structure–activity　properties　difficult.　Here　we　report　a　copper-based　catalyst　with　isolated　active　copper　sites　for　the　hydrogenation　of　CO2　to　methanol.　It　is　revealed　that　the　single-atom　Cu–Zr　catalyst　with　Cu1–O3　units　contributes　solely　to　methanol　synthesis　around　180　°C,　while　the　presence　of　small　copper　clusters　or　nanoparticles　with　Cu–Cu　structural　patterns　are　responsible　for　forming　the　CO　by-product.　Furthermore,　the　gradual　migration　of　Cu1–O3　units　with　a　quasiplanar　structure　to　the　catalyst　surface　is　observed　during　the　catalytic　process　and　accelerates　CO2　hydrogenation.　The　highly　active,　isolated　copper　sites　and　the　distinguishable　structural　pattern　identified　here　extend　the　horizon　of　single-atom　catalysts　for　applications　in　thermal　catalytic　CO2　hydrogenation　and　could　guide　the　further　design　of　high-performance　copper-based　catalysts　to　meet　industrial　demand.　[Figure　not　available:　see　fulltext.]　©　2022,　The　Author(s),　under　exclusive　licence　to　Springer　Nature　Limited.