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Grain boundaries exhibit phase-like behavior in which their structure, chemistry and properties may change discontinuously at critical values of thermodynamic parameters such as temperature, pressure and chemical potential. Therefore, grain boundaries (and other interfaces such as surfaces and heterophase boundaries) can be treated as thermodynamically stable interfacial states. To differentiate these interfacial states from bulk phases, the term “complexion” has been introduced. A variety of terminology has been used to describe complexions and complexion transitions. In many cases, several terms exist that describe essentially the same phenomenon. We give an overview of complexion-related terminology, suggest a preferred nomenclature and discuss a classification framework that can be used to categorize complexions and complexion transitions. The field of grain boundary complexions has evolved rapidly in the past decade due to advances in experimental equipment – in particular, aberration-corrected transmission electron microscopy – and progress in computational simulation methods. Grain boundary complexion transitions are the root cause of a wide variety of materials phenomena – such as abnormal grain growth, grain boundary embrittlement and activated sintering – that have defied mechanistic explanation for years. In this overview, we review the history and theory of grain boundary complexion transitions, their role in materials processing and their effect on materials properties.