The paper summarizes experimental results on the activity and selectivity of high-temperature (T-c) superconductors and some related cuprates in different heterogeneous catalytic reactions (ortho-para hydrogen conversion, iso-propanol and methanol dehydrogenation, nitric oxide decomposition and reduction with carbon monoxide, ammonia oxidation, selective oxidation of methanol and ethanol, partial oxidation of methane and of toluene, ammoxidation of toluene, oxidation of carbon monoxide). It contains also information for the structural peculiarities of YBa2Cu3O7-x superconductors and data for oxygen reactivity from temperature-programmed reduction, oxygen isotopic exchange and oxygen desorption measurements. A distinct correlation between the superconductivity of YBa2Cu3O7-x and its catalytic activity in ortho-para hydrogen conversion is observed. Data in the literature show an influence of the oxygen vacancies concentration in these solids and their activity and selectivity. However, in many cases no relationship seems to exist between the superconducting properties and the catalytic activity and selectivity. This is explained by : (i) the experiments were performed at temperatures much higher than T-c, and (ii) significant surface and bulk alterations in high-T-c superconductors during the catalytic reactions, as concluded from X-ray photoelectron spectroscopy and X-ray diffraction data (appearance of Cu+ and Cu-0 states in the surface layers, orthorhombic/ tetragonal phase transition, and, in some cases, decomposition and phase segregation). The outstanding importance of oxygen binding energy for complete oxidation reactions is already shown. From the practical point of view, the high activities and selectivities should be noted of high-T-c superconductors in selective oxidation of aliphatic alcohols to the corresponding aldehydes, in nitric oxide reduction by carbon monoxide and in ammoxidation of toluene to benzonitrile. Special attention should be paid to some related non-superconducting cuprates, which show high performances for complete oxidation reactions, with specific catalytic activities commensurable to those of the best catalysts known until now (e.g., Pt, Co3O4). Some possible future studies on the catalytic properties of high-T-c superconductors and related cuprates are outlined.