Most micro air vehicles rely heavily on reliable GPS measurements for proper estimation and control, and therefore struggle in GPS-degraded environments. When GPS is not available, the global position and heading of the vehicle is unobservable. This dissertation establishes the theoretical and practical advantages of a relative navigation framework for MAV navigation in GPS-degraded environments. This dissertation explores how the consistency, accuracy, and stability of current navigation approaches degrade during prolonged GPS dropout and in the presence of heading uncertainty. Relative navigation (RN) is presented as an alternative approach that maintains observability by working with respect to a local coordinate frame. RN is compared with several current estimation approaches in a simulation environment and in hardware experiments. While still subject to global drift, RN is shown to produce consistent state estimates and stable control. Estimating relative states requires unique modifications to current estimation approaches. This dissertation further provides a tutorial exposition of the relative multiplicative extended Kalman filter, presenting how to properly ensure observable state estimation while maintaining consistency. The filter is derived using both inertial and body-fixed state definitions and dynamics. Finally, this dissertation presents a series of prolonged flight tests, demonstrating the effectiveness of the relative navigation approach for autonomous GPS-degraded MAV navigation in varied, unknown environments. The system is shown to utilize a variety of vision sensors, work indoors and outdoors, run in real-time with onboard processing, and not require special tuning for particular sensors or environments. Despite leveraging off-the-shelf sensors and algorithms, the flight tests demonstrate stable front-end performance with low drift. The flight tests also demonstrate the onboard generation of a globally consistent, metric, and localized map by identifying and incorporating loop-closure constraints and intermittent GPS measurements. With this map, mission objectives are shown to be autonomously completed.