We review various simplified models that have been advanced to describe layering (complexion) transitions at grain boundaries in multicomponent solids. In particular, we first outline lattice-gas, off-lattice atomistic and thermodynamic models that have been employed to investigate phase-like behavior at segregated grain boundaries. The results of these investigations are summarized in the form of complexion diagrams in different thermodynamic planes, and we highlight important features of these diagrams, such as complexion transition lines and critical points. Finally, we describe current issues and provide a future outlook.