Unmanned aerial vehicles (UAVs) have acquired remarkable popularity, thanks to their variety of applications in numerous domains spanning from surveillance, health to agriculture and smart cities. UAVs are also enabler in wireless communication that has potential features such as ubiquitous and reliable connectivity, fast and easy deployment, adaptive altitude, higher chance of line of sight (LOS) propagation path, higher mobility and flexibility. There are numerous surveys that summarized these advantages for different situations and scenarios. However, none of these surveys discussed the role of UAVs in public safety communications from the energy efficiency perspective. In this paper, we review the existing literature for UAV communication with taking into account the energy consumption criteria, and propose a multi-layered network architecture incorporating UAVs for public safety communication. Future research directions are also discussed. INDEX TERMS UAV, multi-layered architecture, QoS, energy efficiency, public safety communications.