Multi-carrier energy networks (MCENs) have become an engaging research topic during the past few years. Due to the high penetration of renewable energy sources in transmission grids along with the rapid installation of cogeneration units, the interdependency between various energy carriers is increased, and the performance of an individual energy network is exceedingly related to the other ones. Thus, it is inevitable to consider an integrated viewpoint towards the analysis and assessment of energy networks. This paper presents a comprehensive review on MCENs by concentrating on the major contributions in the recent years. An overview on the energy hub concept and its most popular components used in the literature is provided to identify the less utilized devices in this area for further investigations. Then the most popular problems of MCENs are categorized besides their relevant techniques and solutions reported in the literature, focusing on different schemes and with various perspectives. This paves the way for proposing and implementing other well-developed or novel methodologies to cope with these problems. Finally, the future trends of these integrated networks and their main concerns and challenges are discussed for further investigations.