The review summarizes recent experimental results of studying heat transfer on rough surfaces synthesized by plasma. The plasma-surface interaction leads to the stochastic clustering of the surface roughness with a high specific area breaking the symmetry of the virgin surface of the initial crystalline materials. Such a surface is qualitatively different from the ordinary Brownian surface. The micro- and nanostructured surface consist of pores, craters, and nanofibers of size from tens of nanometers to tens of microns, which can provide new heat transfer properties related to a violation of the symmetry of the initial materials. In recent years, new results have been obtained in the study of heat transfer during phase change on plasma-modified surfaces in relation to energy, chemical, and cryogenic technologies. The objective of the review is to describe the specific structure of refractory metals after high-temperature plasma irradiation and the potential application of plasma processing of materials in order to create heat exchange surfaces that provide a significant intensification of two-phase heat transfer. Refractory metals with such a highly porous rough surface can be used as plasma-facing components for operation under extreme heat and plasma loads in thermonuclear and nuclear reactors, as catalysts for hydrogen production, as well as in biotechnology and biomedical applications.