As the specifications of the 5th generation of cellular networks mature, the deployment phase is starting up. Hence, peaks of data rates in the order of tens of Gbit/s as well as more energy efficient deployments are expected. Nevertheless, the quick development of new applications and services encourage the research community to look beyond 5G and explore new technological components. Indeed, to meet the increasing demand for mobile broadband as well as internet of things type of services, the research and standardization communities are currently investigating novel physical and medium access layer technologies, including further virtualization of networks, the use of the lower Terahertz bands, even higher cell densification, and full-duplex (FD) communications. FD has been proposed as one of the enabling technologies to increase the spectral efficiency of conventional wireless transmission modes, by overcoming our prior understanding that it is not possible for radios to transmit and receive simultaneously on the same time-frequency resource. Due to this, we can also refer to FD communications as in-band FD. In-band FD transceivers have the potential of improving the attainable spectral efficiency of traditional wireless networks operating with half-duplex (HD) transceivers by a factor close to two. In addition to the spectral efficiency gains, full-duplex can provide gains in the medium access control layer, in which problems such as the hidden/exposed nodes and collision detection can be mitigated and the energy consumption can be reduced. Until recently, in-band FD was not considered as a solution for wireless networks due to the inherent interference created from the transmitter to its own receiver, the so-called self-interference (SI). However, recent advancements in antenna and analog/digital interference cancellation techniques demonstrate FD transmissions as a viable alternative to traditional HD transmissions. Given the recent architectural progression of 5G towards smaller cells, higher densification, higher number of antennas and utilizing the millimeter wave (mmWave) band, the integration of FD communications into such scenarios is appealing. In-band FD communications are suited for short range communication, and although the SI remains a challenge, the use of multiple antennas and the transmission in the mmWave band are allies that help to mitigate the SI in the spatial domain and provide even more gains for spectral and energy efficiency. To achieve the spectral and energy efficiency gains, it is important to understand the challenges and solutions, which can be roughly divided into resource allocation, protocol design, hardware design and energy harvesting. Hence, FD communications appears as an important technology component to improve the spectral and energy efficiency of current communication systems and help to meet the goals of 5G and beyond. The chapter starts with an overview of FD communications, including its challenges and solutions. Next, a comprehensive literature review of energy efficiency in FD communications is presented along with the key solutions to improve energy efficiency. Finally, we evaluate the key aspects of energy efficiency in FD communications for two scenarios: single-cell with multiple users in a pico-cell scenario, and a system level evaluation with macro- and small-cells with multiple users.