Investigation of heat transfer at supercritical pressures began as early as the 1930s, with the study of free-convection heat transfer to fluids at the near-critical point. In the 1950s, the concept of using supercritical "steam" to increase the thermal efficiency of fossil-fired power plants became an attractive option. Currently, using supercritical "steam" in fossil-fired power plants is the largest industrial application of fluids at supercritical pressures. Near the end of the 1950s and at the beginning of the 1960s, several studies were conducted to investigate the potential of using supercritical water as a coolant in nuclear reactors. The USA and the former USSR extensively studied supercritical heat transfer during the 1950s until the 1980s. Research primarily focused around circular water-cooled tube flow geometry. The primary objectives for using supercritical water as a coolant in nuclear reactors are: (1) to increase the thermal efficiency of modern nuclear power plants, which is currently 30-35%, to approximately 45% or higher, and (2) to decrease the operational and capital costs by eliminating steam generators, steam separators, steam dryers, etc. In support of the development of a supercritical water-cooled nuclear reactor, it is necessary to perform a heat-transfer analysis. As a first step in this process, heat-transfer to supercritical water in bare vertical tubes can be investigated as a conservative approach (in general, heat-transfer in fuel bundles will be enhanced with various types of appendages, i.e., bearing pads, end plates, fins, ribs, spacers, etc.). A comparison of selected supercritical-water heat-transfer correlations has shown that their results may differ from one another by more than 200%. Based on these comparisons, it became evident that there is a need to use a reliable, accurate and wide-range supercritical-water heat-transfer correlation. For this reason, the new or recently updated Mokry et al. (2009) correlation was used in the presented analyses. Other areas exist in which supercritical fluids are used, or will be implemented in the near future. These include, for example, using SuperCritical Water Oxidation (SCWO) technology for the treatment of industrial and military wastes, using carbon dioxide in the Supercritical Fluid Leaching (SFL) method for the removal of uranium from radioactive solid wastes and in the decontamination of surfaces, and using supercritical fluids in chemical and pharmaceutical industries, in such processes as supercritical fluid extraction, supercritical fluid chromatography, polymer processing, and others. The objective of this review is to assess the work performed concerning thermophysical properties and the associated heat transfer and pressure drop at supercritical pressures, based on examples of water and carbon dioxide.