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Modern computational capacity enables the efficient discovery of advanced materials whose complexity far exceeds that of the traditional materials long relied upon by humankind. Among many, multicomponent crystalline materials have drawn significant interest for their compositional diversity and flexibility, providing a broad design space to optimize properties and reduce reliance on scarce elements. At finite temperature, a higher compositional degree of freedom is accompanied by greater configurational complexity on the lattice, owing to the configurational entropy contribution from multicomponents to the free energy minimization. Their corresponding complicated order and disorder phenomena not only govern practical material properties but also offer a fascinating playground for challenging the capability of toolkits owned by computational materials science researchers. Targeting material properties for energy and functional applications in cation-disordered rocksalt-type cathodes and medium-entropy alloys, this thesis integrates a broad spectrum of topics in the computational modeling of order and disorder in multicomponent materials: capabilities of modeling techniques; efficient high-throughput screening that enables statistical evaluation of elemental ordering tendencies; the fundamental understanding of ordering behavior on the face-centered cubic lattice through Monte Carlo mappings; and the uncertainty introduced by the Hubbard correction in density functional theory calculations that affects the accuracy of disordered materials discovery. Finally, a dedicated chapter outlines future work, posing new questions that emerge from the advanced understanding gained in this thesis.
