Flying animals ranging in size from fruit flies to hummingbirds are agile fliers with remarkable maneuverability that surpasses those of human-engineered robotic fliers. Some of the maneuvers, such as escaping from predators, inverted landing and recovery from perturbation, are particularly fast and push the animals to operate at their extreme performance. However, the sensorimotor processes that perform the fast transformation from sensory cues to motor actions are not well understood. In this dissertation, I studied two types of rapid maneuvers in flies and hummingbirds: the in-flight escape and inverted landing, as these two maneuvers demonstrate remarkable agility and are less understood. Following this, I developed a bio-inspired inverted landing strategy on an aerial robot using computationally efficient Relative Retinal Expansion Velocity (RREV) as a visual cue, resembling that of flies. This work studied the maneuverability in flying animals in three folds: (1) theoretical work that modeled and analyzed the limitations of the rotational maneuverability; (2) experimental work that collected and studied the behaviors and underlying sensorimotor mechanism of the inverted landing of flies; and (3) applying the understandings of the maneuvers in biological fliers to robotic fliers. By modeling and analyzing the flight control system of insects and hummingbirds, this work reveals that their maneuverability is limited by multiple factors. For example, fruit flies and hummingbirds have similar degree of maneuverability but the underlying limiting factors are different, as the maneuverability of fruit flies is only limited by neural delays and that of hummingbirds could be limited by all three factors. In addition, the maneuverability also appears to be the highest about the roll axis as it requires the least muscle mechanical power and can tolerate the largest neural delays. Experimental work that collects inverted landing attempts show that successful inverted landing in flies involves a serial sequence of well-coordinated behavioral modules, consisting of an initial upward acceleration followed by rapid body rotation and leg extension, before terminating with a leg-assisted body swing pivoted around legs firmly attached to the ceiling. Statistical analyses suggest that rotational maneuvers are triggered when flies' relative retinal expansion velocity reaches a threshold. Also, flies exhibit highly variable pitch and roll rates, which are strongly correlated to and likely mediated by multiple sensory cues. The inverted landing of flies inspires the design of an inverted landing strategy in a small aerial robot using computationally efficient RREV as a visual cue. Simulation results show that the aerial robot is able to achieve robust inverted landing, and it tends to exploit its maximal maneuverability. In addition to the computational aspects of the landing strategy, the robustness of landing is also dependent strongly on the mechanical design of the landing gear, the upward velocity at the start of body rotation, and timing of rotor shutdown.