This paper addresses the tracking control of quadrotors flying outdoors. Two control laws are combined and tested in real-time experiments. The aircraft attitude and the translational displacement are controlled using the backstepping approach, while the altitude is controlled using the sliding mode control strategy. In both cases, new modifications are introduced with respect to the existing classical algorithms. Concerning the backstepping algorithm, we introduce the dynamical model of the quadrotor in the controller design and this guarantees that the virtual input is bounded. On the other hand, the proposed sliding mode control assures that the vehicle's altitude converges in finite time to the desired reference, even when uncertainties are considered in the system. The proposed controller is tested in an outdoor environment and the experiments highlighted the controllers' reliability. Additionally, the performance of the closed-loop plant with the proposed controllers is compared with the performance given by a proportional-derivative controller.