Abstract: To enhance the technical proficiency in low-carbon planning and optimized operations of integrated energy systems (IES), and to promote the low-carbon transition of energy infrastructures and the development of new power system, we present a comprehensive review in these domains, and summarize the research on the development of modelling, system planning, and operational scheduling of IES. Firstly, we expound the typical architecture, essential equipment, and energy flow properties of IES. Secondly, we discuss the low-carbon planning and operational strategies for IES, along with their critical techniques, including technologies such as stochastic multi-state models, power forecasting, strategies for demand-side management, ancillary services for power grids and its mechanisms for low-carbon operations, as well as optimization models and their algorithmic solutions. It is revealed that planning and operation strategies are crucial in supporting the low-carbon, efficient, and cost-effective operation of IES. It is necessary to further investigate the complex challenges, such as precise modelling and swift resolution of high-dimensional, non-linear, multi-objective, and non-convex problems under uncertainty. Finally, we put forward the prospects in the potential applications of emerging technologies such as artificial intelligence, big data, and the internet of things in electrical sector for the low-carbon planning and management of IES, and sum up technical challenges and key issues.