To achieve a fully autonomous unmanned aerial vehicle (UAV) the vehicle needs a high level of self awareness. At a minimum it needs to know where it is and where it wants to go. Computer vision (CV) is a logical solution to this problem. However, using CV to solve motion control problems for UAVs is a challenging problem as both the quadrotor dynamics and camera kinematics are nonlinear. Although both CV and UAVs are not new topics there are relatively few fully autonomous experimental results due to the difficulty in building and maintaining an experimental platform and the high computation power required by many CV algorithms. Recent advances in embedded computers have notably changed the field. This thesis focuses on three important areas:​ developing a reliable and powerful UAV platform for testing bleeding edge CV algorithms, dynamic image-based visual servoing (DIBVS), and monocular visual state estimation (VSE). In order to efficiently perform experimental research on nonlinear control and CV, we developed the indoor Applied Nonlinear Control Lab (ANCL) quadrotor platform. The design for our experimental platform was inspired from other indoor flight test stands and we have prioritized open-source hardware and open-source software. In addition to building the platform we derived a kinematic and dynamic model of a quadrotor and then experimentally identified the system parameters. Also, using a series of experiments we characterized the performance of the wireless communication network between the quadrotor and the motion capture system (MCS) to improve the onboard position control. This thesis proposes several DIBVS control laws for a quadrotor equipped with a single fixed onboard camera. The motion control problem is to regulate the relative position and yaw of the vehicle to a target located on the ground. The control law is termed dynamic as it based on the dynamics and kinematics of the vehicle. The proposed designs use a nonlinear change of state coordinates, the virtual camera method, adaptive control techniques, and image features. The control laws developed have proven convergence rates. Simulation and experimental results demonstrate the methodsâ ease of onboard implementation, performance, and robustness. Next, in this thesis we develop a visual odometry (VO) system which is an onboard CV-based navigation system. An important feature of VO systems is that they are independent of a global navigation satellite system (GNSS). Our approach uses inertial sensor measurements along with scaled position measurements from an onboard CV system which implements a visual simultaneous localization and mapping (VSLAM) system. We study the observability of the visual inertial simultaneous localization and mapping (VISLAM) problem using a state transformation that puts the system into linear time-varying (LTV) form and simplifies the observability analysis. This leads to an observer design with sufficient conditions for convergence. The observer fuses an accelerometer measurement from an inertial measurement unit (IMU) with scaled position measurements from a VSLAM system to estimate vehicle position and velocity. Our approach does not require an approximate linearization of the model equations whereas typical solutions in the literature use an extended Kalman filter (EKF) that linearizes the model equations. Simulations and experimental results onboard a quadrotor UAV validate the proposed designs.