This paper presents the design and development of autonomous attitude stabilization, navigation in unstructured, GPS-denied environments, aggressive landing on inclined surfaces, and aerial gripping using onboard sensors on a low-cost, custom-built quadrotor. The development of a multi-functional micro air vehicle (MAV) that utilizes inexpensive off-the-shelf components presents multiple challenges due to noise and sensor accuracy, and there are control challenges involved with achieving various capabilities beyond navigation. This paper addresses these issues by developing a complete system from the ground up, addressing the attitude stabilization problem using extensive filtering and an attitude estimation filter recently developed in the literature. Navigation in both indoor and outdoor environments is achieved using a visual Simultaneous Localization and Mapping (SLAM) algorithm that relies on an onboard monocular camera. The system utilizes nested controllers for attitude stabilization, vision-based navigation, and guidance, with the navigation controller implemented using a nonlinear controller based on the sigmoid function. The efficacy of the approach is demonstrated by maintaining a stable hover even in the presence of wind gusts and when manually hitting and pulling on the quadrotor. Precision landing on inclined surfaces is demonstrated as an example of an aggressive maneuver, and is performed using only onboard sensing. Aerial gripping is accomplished with the addition of a secondary camera, capable of detecting infrared light sources, which is used to estimate the 3D location of an object, while an under-actuated and passively compliant manipulator is designed for effective gripping under uncertainty.The quadrotor is therefore able to autonomously navigate inside and outside, in the presence of disturbances, and perform tasks such as aggressively landing on inclined surfaces and locating and grasping an object, using only inexpensive, onboard sensors.