The researches on interfacial thermal contact resistance between inorganic solids and polymers have been paid more and more attention in recent years. In this paper, the mechanism of interfacial heat transfer and the measurement approaches on interfacial thermal contact resistance of polymer-based materials are reviewed. Currently, many scholars have established different thermal contact resistance models from macroscopic and microscopic perspective to study the heat transfer mechanism of solid-polymer contact thermal resistance. However, the heat transfer mechanism is complex due to many factors affecting thermal contact resistance. Presently, there are still many difficulties and challenges in the research of solid-polymer thermal contact resistance. For the measurement of interfacial thermal contact resistance of polymer-based materials, novel characterization methods and techniques of micro/nano-scale materials, such as polymer films, have become one of the international research frontiers. This paper mainly introduces the technical methods such as 3ω method and time-domain thermoreflectance method which can be used to characterize the thermal contact resistance between solids and polymers. In addition, the research progresses of polymer-based interface materials in recent years have been also introduced. The polymer based interfacial materials are reviewed and compared based on the types of molecular forces (van der Waals force, covalent bond and non-covalent strong force). Finally, the future research directions of interfacial thermal management are overviewed.