In this paper, we present details of the real time implementation onboard a quadrotor helicopter of learning-based model predictive control (LBMPC). LBMPC rigorously combines statistical learning with control engineering, while providing levels of guarantees about safety, robustness, and convergence. Experimental results show that LBMPC can learn physically based updates to an initial model, and how as a result LBMPC improves transient response performance. We demonstrate robustness to mis-learning. Finally, we show the use of LBMPC in an integrated robotic task demonstration---The quadrotor is used to catch a ball thrown with an a priori unknown trajectory.