This paper focuses on the problem of robust control of unmanned rotorcrafts against external disturbances, towards achieving their efficient and safe utilization in real-life challenging applications. Relying on state space representations that incorporate the effects of external disturbances and may be applied in most rotorcraft configurations, the basis for robust control is derived. Employing such models, a receding horizon control strategy that uses the minimum peak performance measure is developed, such that it ensures the minimum possible deviation from the reference for the worst-case disturbance, as well as robust satisfaction of the imposed state and input constraints. Furthermore, proper augmentation of the proposed framework allows the incorporation of obstacle avoidance capabilities. Employing multi-parametric methods the controller is computed explicitly and therefore enables fast real-time execution. The efficiency of the robust predictive control law is evaluated using experimental studies on two different unmanned rotorcraft configurations. The presented experiments include trajectory tracking subject to atmospheric disturbances, slung load operations, collisions handling as well as avoidance of known obstacles.