Eye-based interaction has commonly been based on estimation of eye gaze direction, to locate objects for interaction. We introduce Pursuits, a novel and very different eye tracking method that instead is based on following the trajectory of eye movement and comparing this with trajectories of objects in the field of view. Because the eyes naturally follow the trajectory of moving objects of interest, our method is able to detect what the user is looking at, by matching eye movement and object movement. We illustrate Pursuits with three applications that demonstrate how the method facilitates natural interaction with moving targets.