The development of the high entropy alloys (HEAs) is amongst the most important topics in the field of materials science during the last two decades. The concept of multicomponent, near-equimolar systems has been already applied to the number of other systems, including oxides, carbides, diborides, silicides, and it can be expected that other groups of materials will follow. One of the main driving forces for the development of HEAs is the so-called “four core effects”: high entropy effects, severe lattice distortion, cocktail effect, and sluggish diffusion effect. Their existence and extent has been a subject of heated discussion. Probably the least studied of them is the sluggish diffusion effect, which is of the, especially, high importance from the point of view of the most possible applications of HEAs—as high-temperature materials. Its alleged existence carries a promise of obtaining materials with superior mechanical properties, higher creep resistance, and less susceptibility to high-temperature corrosion. In the current review, the state-of-the-art of diffusion studies in HEAs was presented, as well as the resulting conclusions concerning the existence of the sluggish diffusion effect. Based on the literature analysis, it can be stated that there is no experimental evidence, which would support the existence of the sluggish diffusion in HEAs on the level of tracer and self-diffusivities. Nevertheless, it can be pointed out that our current state of knowledge on the diffusion in HEAs is still far from complete; therefore, further directions of studies are proposed.
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