A key challenge for future energy systems is how to minimize the effects of employing demand response (DR) programs on the consumer. There exists a diverse range of consumers with a variety of types of loads, such as must-run loads, and this can reduce the impact of consumer participation in DR programs. Multi-energy systems (MES) can solve this issue and have the capability to reduce any discomfort faced by all types of consumers who are willing to participate in the DRPs. In this paper, the most recent implementations of DR frameworks in the MESs are comprehensively reviewed. The DR modelling approach in such energy systems is investigated and the main contributions of each of these works are included. Notably, the amount of research in MES has rapidly increased in recent years. The majority of the reviewed works consider power, heat and gas systems within the MES. Over three-quarters of the papers investigated consider some form of energy storage system, which shows how important having efficient, cost-effective and reliable energy storage systems will be in the future. In addition, a vast majority of the works also considered some form of demand response programs in their model. This points to the need to make participating in the energy market easier for consumers, as well as the importance of good communication between generators, system operators, and consumers. Moreover, the emerging topics within the area of MES are investigated using a bibliometric analysis to provide insight to other researchers in this area.