Integrated energy systems (IESs), in which various energy flows are interconnected and coordinated to release potential flexibility for more efficient and secure operation, have drawn increasing attention in recent years. In this article, an integrated energy management system (IEMS) that performs online analysis and optimization on coupling energy flows in an IES is comprehensively introduced. From the theory perspective, an energy circuit method (ECM) that models natural gas networks and heating networks in the frequency domain is discussed. This method extends the electric circuit modeling of power systems to IESs and enables the IEMS to manage large-scale IESs. From the implementation perspective, the architecture design and function development of the IEMS are presented. Tutorial examples with illustrative case studies are provided to demonstrate its functions of dynamic state estimation, energy flow analysis, security assessment and control, and optimal energy flow. From the application perspective, real-world engineering demonstrations that apply IEMSs in managing building-scale, park-scale, and city-scale IESs are reported. The economic and environmental benefits obtained in these demonstration projects indicate that the IEMS has broad application prospects for a low/zero-carbon future energy system.