Due to the growing impact of the information and communications technology (ICT) sector on electricity usage and greenhouse gas emissions, telecommunication networks require new solutions which will enable the improvement of the energy efficiency of networks. Access networks, which are responsible for the last mile of connectivity and also for one of the largest shares in network energy consumption, are viable candidates for the implementation of new protocols, models and methods which will contribute to the reduction of the energy consumption of such networks. Among the different types of access networks, hybrid fiber–wireless (FiWi) networks are a type of network that combines the capacity and reliability of optical networks with the flexibility and availability of wireless networks, and as such, FiWi networks have begun to be extensively used in modern access networks. However, due to the advent of high-bandwidth applications and Internet of Things networks, the increased energy consumption of FiWi networks has become one of the most concerning challenges required to be addressed. This paper provides a comprehensive overview of the progress in approaches for improving the energy efficiency (EE) of different types of FiWi networks, which include the radio-and-fiber (R&F) networks, the radio-over-fiber networks (RoF), the FiWi networks based on multi-access edge computing (MEC) and the software-defined network (SDN)-based FiWi networks. It also discusses future directions for improving the EE in the FiWi networks.