The development of high-energy-density batteries, advanced sensor technologies, and advanced control algorithms for multirotor electric vertical takeoff and landing (eVTOL) unmanned aerial vehicles (UAVs) has led to interest in using these vehicles for a variety of applications including surveillance, package delivery, and even human transportation. In each of these cases, the ideal vehicle is one that can maneuver in congested spaces, but is efficient for traveling long distances. The combination of wings and vectored thrust make winged eVTOLs the obvious choice. However, these aircraft experience a much wider range of flight conditions that makes them challenging to model and control. This thesis contributes an aerodynamic model and a planning and control method for small, 1-2 m wingspan, winged eVTOLs. We develop the aerodynamic model based on first-principles, lumped-element aerodynamics, extending the lift and drag models to consider high-angle-of-attack flight conditions using models proposed in the literature. We present two methods for generating spline trajectories, one that uses the singular value decomposition to find a minimum-derivative polynomial spline, and one that uses B-splines to produce trajectories in the convex hull of a set of waypoints. We compare the quality of trajectories produced by both methods. Current control methods for winged eVTOL UAVs consider the vehicle primarily as a fixed-wing aircraft with the addition of vertical thrust used only during takeoff and landing. These methods provide good long-range flight handling but fail to consider the full dynamics of the vehicle for tracking complex trajectories. We present a trajectory tracking controller for the full dynamics of a winged eVTOL UAV in hover, fixed-wing, and partially transitioned flight scenarios. We show that in low- to moderate-speed flight, trajectory tracking can be achieved using a variety of pitch angles. In these conditions, the pitch of the vehicle is a free variable that we use to minimize the necessary thrust, and therefore energy consumption, of the vehicle. We use a geometric attitude controller and an airspeed-dependent control allocation scheme to operate the vehicle at a wide range of airspeeds, flight path angles, and angles of attack. We provide theoretical guarantees for the stability of the proposed control scheme assuming a standard aerodynamic model, and we present simulation results showing an average tracking error of 20 cm, an average computation rate of 800 Hz, and an 85% reduction in tracking error versus using a multirotor controller for low-speed flight.