The Internet of Things (IoT) has been the key to many advancements in next-generation technologies for the past few years. With a conceptual grouping of ecosystem elements such as sensors, actuators, and smart objects connected together, complex operations like environmental monitoring, intelligent transport systems, smart buildings, and smart cities are able to be performed. Edge computing technology extends the reach/scope of IoT ecosystems, offering robust and powerful computational capabilities by connecting multiple devices through the Internet. Unfortunately, this form of computation comes with a significant drawback with strict energy constraints and low power efficiency, which highly limits its potential and usage. In this paper, we present some of the challenges in the planning of energy-efficient IoT edge devices and discuss some of the recent research efforts that proposed promising solutions that address these challenges. Specifically, we first analyze the challenges and reasons for improving the energy consumption of edge platforms and IoT devices. Next, we perform case studies that outline the energysaving techniques in smart grids, smart cities, electric vehicles (EV), smart home devices, and Virtual Reality and Augmented Reality (VR/AR). We further discuss different approaches such as computation offloading, edge devices hardware and software designs, and a number of algorithms that help reduce energy consumption. Finally, we outline possible future directions and our vision of improving energy efficiency on edge platforms.