As integrated energy systems (IES) continue to undergo development and advancement, the degree of coupling between subsystems and their complexity are also on the rise, posing a challenge for the reliability assessment of such systems. The conventional method is unable to explain the interaction between subsystems as well as system-level phenomena. The complex network theory is needed to provide a deeper analysis. Firstly, this paper introduces the basic concept and analysis tools of complex network theory. Secondly, the topological network model and the identification indexes of weak links for the IES are summarized as the basis for reliability assessment. Then, the reliability assessment indexes and assessment methods are sorted out for the IES based on the complex network theory; and further, the measures to optimize the reliability of the IES are put forward. Finally, from the perspective of complex network theory, directions for future research on the reliability assessment of IES are suggested.