The study of the transition from high-entropy alloys (HEAs) to conventional alloys (CAs) composed of the same alloying components is apparently important, both for understanding the formation of HEAs and for proper evaluation of their potential with respect to that of the corresponding CAs. However, this transition has thus far been studied in only two types of alloy systems: crystalline alloys of iron group metals (such as the Cantor alloy and its derivatives) and both amorphous (a-) and crystalline alloys, TE-TL, of early (TE = Ti, Zr, Nb, Hf) and late (TL = Co, Ni, Cu) transition metals. Here, we briefly overview the main results for the transition from HEAs to CAs in these alloy systems and then present new results for the electronic structure (ES), studied with photoemission spectroscopy and specific heat, atomic structure, thermal, magnetic and mechanical properties of a-TE-TL and Cantor-type alloys. A change in the properties of the alloys studied on crossing from the HEA to the CA concentration range mirrors that in the ES. The compositions of the alloys having the best properties depend on the alloy system and the property selected. This emphasizes the importance of knowing the ES for the design of new compositional complex alloys with the desired properties.