The implementation of Internet-of-Things (IoT) applications faces several challenges in practice, such as compliance with Quality-of-Service requirements, resource constraints, and energy consumption. In this context, the joint edge–cloud paradigm for IoT applications can resolve some of the issues arising in pure cloud computing scenarios, such as those related to latency, energy, or privacy. Therefore, an edge–cloud environment could be promising for resource and energy-efficient IoT applications that implement virtual network functions (VNFs) bound together into service function chains (SFCs). However, a resource and energy-efficient SFC placement requires smart SFC embedding mechanisms in the edge–cloud environment, as several challenges arise, such as IoT service chain modeling and evaluation, the tradeoff between resource allocation, energy efficiency and performance, and the resource dynamics. In this article, we address issues in modeling resource and energy utilization for IoT applications in edge–cloud environments. A smart traffic monitoring IP camera system is deployed as a use case for a realistic modeling of a service chain. The system is implemented in our testbed, which is designed and developed specifically to model and investigate the resource and energy utilization of SFC embedding strategies. A resource and energy-aware SFC strategy in the edge–cloud environment for IoT applications is then proposed. Our algorithm is able to cope with dynamic load and resource situations emerging from dynamic SFC requests. The strategy is evaluated systematically in terms of the acceptance ratio of SFC requests, resource efficiency and utilization, power consumption, and VNF migrations depending on the offered system load. Results show that our strategy outperforms some existing approaches in terms of resource and energy efficiency, thus it overcomes the relevant challenges from practice and meets the demands of IoT applications.