Unmanned aerial vehicles (UAVs) are emerging as enablers for supporting many applications and services, such as precision agriculture, search and rescue, temporary network deployment, coverage extension, and security. UAVs are being considered for integration into emerging wireless networks as aerial users, aerial relays (ARs), or aerial base stations (ABSs). This dissertation proposes employing UAVs to contribute to physical layer techniques that enhance the security performance of advanced wireless networks and services in terms of availability, resilience, and confidentiality. The focus is on securing terrestrial cellular communications against eavesdropping with a cellular-connected UAV that is dispatched as an AR or ABS. The research develops mathematical tools and applies machine learning algorithms to jointly optimize UAV trajectory and advanced communication parameters for improving the secrecy rate of wireless links, covering various communication scenarios: static and mobile users, single and multiple users, and single and multiple eavesdroppers with and without knowledge of the location of attackers and their channel state information. The analysis is based on established air-to-ground and air-to-air channel models for single and multiple antenna systems while taking into consideration the limited on-board energy resources of cellular-connected UAVs. Simulation results show fast algorithm convergence and significant improvements in terms of channel secrecy capacity that can be achieved when UAVs assist terrestrial cellular networks as proposed here over state-of-the-art solutions. In addition, numerical results demonstrate that the proposed methods scale well with the number of users to be served and with different eavesdropping distributions. The presented solutions are wireless protocol agnostic, can complement traditional security principles, and can be extended to address other communication security and performance needs.