Multirotor systems have traditionally been employed for missions that ensure minimal contact with the objects in their vicinity. However, their agile flight dynamics lets them sense, plan and react rapidly, and therefore perform highly dynamic missions. In this work, we push their operational envelope further by developing a complete framework that allows a multirotor to dock with a moving platform. Our approach builds on state-of-the-art and optimal methods for estimating and predicting the state of the moving platform, as well as for generating interception trajectories for the docking multirotor. Through a total of 25 field tests outdoors, we demonstrate the capabilities of our system in docking with a platform moving at different speeds and in various operating conditions. We also evaluate the quality of our system’s trajectory following at speeds over 2 m/s to effect docking within 10 s.