Heterogeneous Internet of Things (HetIoT) is an emerging research field that has strong potential to transform both our understanding of fundamental computer science principles and our future living. HetIoT is being employed in increasing number of areas, such as smart home, smart city, intelligent transportation, environmental monitoring, security systems, and advanced manufacturing. Therefore, relaying on strong application fields, HetIoT will be filled in our life and provide a variety of convenient services for our future. The network architectures of IoT are intrinsically heterogeneous, including wireless sensor network, wireless fidelity network, wireless mesh network, mobile communication network, and vehicular network. In each network unit, smart devices utilize appropriate communication methods to integrate digital information and physical objects, which provide users with new exciting applications and services. However, the complexity of application requirements, the heterogeneity of network architectures and communication technologies impose many challenges in developing robust HetIoT applications. This paper proposes a four-layer HetIoT architecture consisting of sensing, networking, cloud computing, and applications. Then, the state of the art in HetIoT research and applications have been discussed. This paper also suggests several potential solutions to address the challenges facing future HetIoT, including self-organizing, big data transmission, privacy protection, data integration and processing in large-scale HetIoT.