In this review, we analyze the structure of multicomponent alloys without principal components (they are also called high entropy alloys—HEAs), containing not only metals but also hydrogen, nitrogen, carbon, boron, or silicon. In particular, we discuss the phenomenon of grain boundary (GB) wetting by the melt or solid phase. The GB wetting can be complete or incomplete (partial). In the former case, the grains of the matrix are completely separated by the continuous layer of the second phase (solid or liquid). In the latter case of partial GB wetting, the second solid phase forms, between the matrix grains, a chain of (usually lenticular) precipitates or droplets with a non-zero value of the contact angle. To deal with the morphology of GBs, the new GB tie-lines are used, which can be constructed in the two- or multiphase areas of the multidimensional HEAs phase diagrams. The GBs in HEAs in the case of complete or partial wetting can also contain hydrides, nitrides, carbides, borides, or silicides. Thus, GB wetting by the hydrides, nitrides, carbides, borides, or silicides can be used in the so-called grain boundary chemical engineering in order to improve the properties of respective HEAs.