Unmanned aerial vehicles (UAVs) have become very popular for many military and civilian applications including in agriculture, construction, mining, environmental monitoring, etc. A desirable feature for UAVs is the ability to navigate and perform tasks autonomously with least human interaction. This is a very challenging problem due to several factors such as the high complexity of UAV applications, operation in harsh environments, limited payload and onboard computing power and highly nonlinear dynamics. Therefore, more research is still needed towards developing advanced reliable control strategies for UAVs to enable safe navigation in unknown and dynamic environments. This problem is even more challenging for multi-UAV systems where it is more efficient to utilize information shared among the networked vehicles. Therefore, the work presented in this report contributes towards the state-of-the-art in UAV control for safe autonomous navigation and motion coordination of multi-UAV systems. The first part of this report deals with single-UAV systems. Initially, a hybrid navigation framework is developed for autonomous mobile robots using a general 2D nonholonomic unicycle model that can be applied to different types of UAVs, ground vehicles and underwater vehicles considering only lateral motion. Then, the more complex problem of three-dimensional (3D) collision-free navigation in unknown/dynamic environments is addressed. To that end, advanced 3D reactive control strategies are developed adopting the sense-and-avoid paradigm to produce quick reactions around obstacles. A special case of navigation in 3D unknown confined environments (i.e. tunnel-like) is also addressed. General 3D kinematic models are considered in the design which makes these methods applicable to different UAV types in addition to underwater vehicles. Moreover, different implementation methods for these strategies with quadrotor-type UAVs are also investigated considering UAV dynamics in the control design. Practical experiments and simulations were carried out to analyze the performance of the developed methods. The second part of this report addresses safe navigation for multi-UAV systems. Distributed motion coordination methods of multi-UAV systems for flocking and 3D area coverage are developed. These methods offer good computational cost for large-scale systems. Simulations were performed to verify the performance of these methods considering systems with different sizes.