This thesis presents contributions to the state-of-the-art in quadrotor control, payload transportation with single and multiple quadrotors, and trajectory generation for single and multiple quadrotors. In Ch. 2 we describe a controller capable of handling large roll and pitch angles that enables a quadrotor to follow trajectories requiring large accelerations and also recover from extreme initial conditions. In Ch. 3 we describe a method that allows teams of quadrotors to work together to carry payloads that they could not carry individually. In Ch. 4 we discuss an online parameter estimation method for quadrotors transporting payloads which enables a quadrotor to use its dynamics in order to learn about the payload it is carrying and also adapt its control law in order to improve tracking performance. In Ch. 5 we present a trajectory generation method that enables quadrotors to fly through narrow gaps at various orientations and perch on inclined surfaces. Chapter 6 discusses a method for generating dynamically optimal trajectories through a series of predefined waypoints and safe corridors and Ch. 7 extends that method to enable heterogeneous quadrotor teams to quickly rearrange formations and avoid a small number of obstacles.