The need to restructure the current energy systems is a result of growing environmental issues, a shortage of fossil fuel resources, unchecked demand growth, and the development of effective multi-generation systems. Multi-energy systems that are feasible will be used as energy sources in the future. Shifting to low or zero-carbon energy carriers requires a major transformation in the energy system. Multi-carrier energy systems (MCE) are capable of efficient and flexible operation when they are deployed to meet various load demands (heating, cooling, and electrical demands). In this article, the concept of a multi-carrier energy system based on the literature considering its objective, topology, and framework has been discussed. Further, modeling of multi-carrier energy systems considering combined heat and power (CHP), energy storage, chiller, boiler, and power to gas (P2G) has been explored from the literature. Also, various optimization techniques considering its objective function have been reviewed.