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The increasing prominence of data centers (DCs) in the global digital economy has raised concerns about energy consumption and carbon emissions. Simultaneously, the rapid advancement of integrated energy systems (IES) has enabled DCs to efficiently harness clean energy and waste heat, contributing to sustainability. A concept of data center integrated energy system (DC-IES) is introduced in this paper, and its generalization, approaches, methods, techniques, and future perspectives are scrutinized on the utilization of renewable energy, recovery of waste heat, construction of producer and consumer and diversity of system architecture, as well as optimization solutions in DC-IES planning and design. The evaluation indicators and optimization objectives of DC-IES are also discussed from perspectives of energy, water, economy, environment and reliability. Furthermore, innovative models are proposed for DC-IES to actively engage in the interaction between computing networks and power grids as well as heating networks respectively, while also emphasizing their associated research through the technical principles, participating elements and benefit impacts. It reveals that the integration of non-interactive workloads in the computing network, along with the utilization of flexible resources from diesel generators and uninterruptible power supply, as well as the implementation of waste heat recovery technologies such as heat pumps and absorption refrigeration systems, will significantly enhance the planning and operation of DC-IES. Finally, a series of challenges and future perspectives related to the reliability and cost-effectiveness encountered in the optimization of DC-IES are revealed.