The development of Internet of Things (IoT) technology enables the rapid growth of connected smart devices and mobile applications. However, due to the constrained resources and limited battery capacity, there are bottlenecks when utilizing the smart devices. Mobile edge computing (MEC) offers an attractive paradigm to handle this challenge. In this work, we concentrate on the MEC application for IoT and deal with the energy saving objective via offloading workloads between cloud and edge. In this regard, we firstly identify the energy-related challenges in MEC. Then we present a green-aware framework for MEC to address the energy-related challenges, and provide a generic model formulation for the green MEC. We also discuss some state-of-the-art workloads offloading approaches to achieve green IoT and compare them in comprehensive perspectives. Finally, some future research directions related to energy efficiency in MEC are given.