The Internet of Things connects a large number of smart mobile devices with the Internet, where these devices are embedded with often limited communication, computation, and caching resources. To address the heterogeneity of these devices and achieve efficient overall system resource utilization, researchers have proposed various device-to-device resource sharing models, enabling mobile devices to form device-todevice connections and to share their resources for cooperative task execution. Most of these existing works, however, considered scenarios where mobile devices can share one or two types of resources, and hence inadequately explore the potential of resource sharing among mobile devices. In this article, we introduce a general framework where mobile devices can share any combination of the three types of resources, and it can generalize many existing deviceto- device resource sharing models. In addition, it can achieve more efficient resource allocation by offering mobile devices more flexibility in terms of resource sharing. Based on the proposed framework, we focus on discussing two issues: the optimization issue, regarding how to schedule resources among devices; and the economic issue, regarding how to motivate the device owners to share their resources. We introduce the challenges and potential solutions to these two issues. We further outline several open issues and future directions for the proposed general resource sharing framework.