Heterogeneous　catalytic　ozonation　(HCO)　becomes　a　promising　advanced　oxidation　process　for　water　purification　due　to　its　strong　portability　and　applicability.　Although　many　efforts　have　been　made　to　explore　the　radical-based　catalytic　mechanism　in　traditional　HCO　processes,　they　are　susceptible　to　co-existing　impurities　in　natural　water.　Hence,　achieving　non-radical　and　selective　oxidation　in　the　catalyst　surface　region　is　an　important　strategy　to　overcome　this　bottleneck　and　attain　high　chemical　utilization　efficiency.　Despite　a　handful　of　studies　having　been　conducted　for　the　non-radical　ozonation　system,　the　associated　mechanism　has　not　been　fully　elucidated　yet.　In　this　perspective,　the　surface　coordination　species　in　different　HCO　catalysts　are　deliberately　discussed,　including　(1)　surface-adsorbed　H2O　or　surface-OH,　(2)　surface-adsorbed　oxygen　species,　and　(3)　surface-organic-O3　complex.　The　limitations　and　prospects　of　these　surface　coordination　species　in　HCO　were　highlighted　to　arouse　attention　in　future　applications.