The objective of this thesis is the design, build and testing of a morphing UAV with a continuous variable trailing edge. This morphing UAV is inspired by the Variable Camber Continuous Trailing Edge Flap (VCCTEF) aircraft conceptualized by NASA. The morphing UAV shares several, but not all, features of the VCCTEF. It has a continuous trailing edge flap made up of 5 sections per wing, with each section driven by a servo-actuator and capable of actively controlling the shape of the trailing edge. The UAV is tested in the wind tunnel, and aerodynamic data determined. Controller designs that determine the optimal configuration of the trailing edge for drag minimization during cruise, and lift maximization during takeoff, are discussed, and closed loop simulations with these designs are presented.