This paper presents a review and evaluation of a large body of the latest published literature, especially since 1989, on the use of ternary composition diagrams and residue curve maps (RCMs), in particular, for the heuristic synthesis and shortcut design of multicomponent separation processes, with emphasis on azeotropic systems. RCMs and analogous liquid/liquid and solid/liquid phase diagrams are significant design tools, because they can represent good approximations to actual equilibrium behavior and can be used to predict composition changes in separation processes involving vapor/liquid mixtures (e.g., azeotropic, extractive, and reactive distillations), liquid/liquid mixtures (e.g., extraction), and solid/liquid mixtures (e.g., extractive crystallization). We describe how to construct RCMs from minimal data, as well as how to represent separation operations on ternary diagrams. We illustrate the use of ternary diagrams including RCMs for the feasibility analysis, flowsheet development, and preliminary design of both homogeneous and heterogeneous separation processes, particularly involving azeotropic systems. Our discussion emphasizes the design applications of the published results, as well as the proper clarifications of some traditional misconceptions and contradicting recommendations reported in the literature. Given the fundamental and practical insights into various aspects of separation process synthesis that can be gained from ternary diagrams including RCMs, we suggest that they are of great value to practicing chemical engineers and in undergraduate design teaching.