Recent discoveries of multicomponent concentrated solid-solution alloys hold promise for enhanced properties—such as enhanced mechanical properties, radiation tolerance, high temperature strength, corrosion resistance and some novel functional properties, provide a new strategy for alloy design using extreme disorder. Yet, deep understanding of these intriguing properties is complicated by the very effects of disorder that make them interesting. All the desirable properties of these alloys ultimately originate from the disorder-induced properties of underlying electronic structure, lattice dynamics, and thermodynamics. Therefore, understanding the disorder-induced fundamental physical properties is prerequisite for the science-based design of this class of alloys for practical applications. Here, we elucidate the role of extreme (maximal) substitutional disorder plays in the fundamental physics of disordered alloys and review the recently developed theoretical methodologies in modeling the basic physical properties, particularly electronic structure, magnetism, electrical transport, and lattice vibrations in multicomponent concentrated solid-solution alloys.