Restructuring the power system with higher penetration of distributed energy resources (DERs) and intelligent devices offers the potential for more efficient, reliable, and better resource utilisation of power systems through the transactive energy framework (TEF). This article provides a general overview of the mathematical models and formulations of the TEF reported in the literature. TEF concepts can be applied to various levels of the power system. Here, the TEF-related literature is divided into individual DER-, building-, microgrid-, and macrogrid-level TEF. The mathematical models of transactive agents corresponding to each level and power system network models are presented. Furthermore, TEF models for energy management and trading of integrated multi-energy systems are analysed. Finally, the potential challenges and future research directions for transactive energy are discussed.