Multi-access edge computing (MEC) has recently been proposed to aid mobile end devices in providing compute- and data-intensive services with low latency. Growing service demands by the end devices may overwhelm MEC installations, while cost constraints limit the increases of the installed MEC computing and data storage capacities. At the same time, the ever increasing computation capabilities and storage capacities of mobile end devices are valuable resources that can be utilized to enhance the MEC. This article comprehensively surveys the topic area of device-enhanced MEC, i.e., mechanisms that jointly utilize the resources of the community of end devices and the installed MEC to provide services to end devices. We classify the device-enhanced MEC mechanisms into mechanisms for computation offloading and mechanisms for caching. We further subclassify the offloading and caching mechanisms according to the targeted performance goals, which include throughput maximization, latency minimization, energy conservation, utility maximization, and enhanced security. We identify the main limitations of the existing device-enhanced MEC mechanisms and outline future research directions.