With the in-depth researches of new technologies or methods such as 5G, software defined networking (SDN), named data networks (NDN), and mobile edge computing or fog computing, Internet of Things (IoT) applications undergo further advancement. In an environment of variety of application scenarios, high quality of service and universal participation of objects, data forwarding models based on traditional wireless sensor networks (WSN) that is the subset of IoT cannot fully adapt to meet the needs. Therefore, in order to guarantee the successive of IoT services, it is the most basic problem and research interest to develop data forwarding mechanism more suitable for IoT. First, in this paper, the architecture of IoT and the key problems of data forwarding in IoT are analyzed. Second, a number of representative studies of data forwarding for IoT are classified. Then, for the chosen typical data forwarding models in different IoT scenarios, their mathematic methods, merits and shortcomings are reviewed along with a comparison of the models in many aspects. Finally, the research problems are analyzed in detail and some future development directions are suggested. In summary, this study shows that the emergence of the new technologies, such as 5G, brings the opportunities and challenges for the research of data forwarding model in IoT. Thus, the key emphasis in future work will be the theoretical research of the model and method of energy-efficient of data forwarding in IoT in providing a solid foundation for the practical applications.