Grain boundaries (GBs) can undergo first-order or continuous phase-like transitions, which are called complexion transitions. Such GB transitions can cause abrupt changes in transport and physical properties, thereby critically influencing sintering, grain growth, creep, embrittlement, electrical/thermal/ionic conductivity, and a broad range of other materials properties. Specifically, the presence of multiple dopants and impurities can significantly alter the GB complexion formation and transition. This article reviews and discusses several GB adsorption (segregation) and prewetting/premelting type complexion models in multicomponent alloys, in which the interactions among multiple adsorbates not only provide a route to control GB properties but also produce novel phenomena. Specifically, various ternary GB diagrams, including both GB adsorption complexion diagrams with well-defined transition lines calculated from a lattice model (without considering interfacial disordering) and GB diagrams that predict useful trends for average general GBs to disorder at high temperatures and related sintering phenomena, are constructed to quantitatively describe the GB behaviors as functions of bulk compositions. Finally, we propose a new opportunity of utilizing "high-entropy GB complexions" to stabilize nanocrystalline alloys.