With the development of wireless technology, various emerging mobile applications are attracting significant attention and drastically changing our daily lives. Applications such as augmented reality and object recognition demand stringent delay and powerful processing capability, which exerts enormous pressure on mobile devices with limited resources and energy. In this article, a survey of techniques for mobile device energy optimization is presented in a hierarchy of device design and operation, computation offloading, wireless data transmission, and cloud execution of offloaded computation. Energy management strategies for mobile devices from hardware and software aspects are first discussed, followed by energy-efficient computation offloading frameworks for mobile applications that trade application response time for device energy consumption. Then, techniques for efficient wireless data communication to reduce transmission energy are summarized. Finally, the execution mechanisms of application components or tasks in various clouds are further described to provide energy-saving opportunities for mobile devices. We classify the research works based on key characteristics of devices and applications to emphasize their similarities and differences. We hope that this survey will give insights to researchers into energy management mechanisms on mobile devices, and emphasize the crucial importance of optimizing device energy consumption for more research efforts in this area.