In this paper we address the integrated prediction, planning, and control problem that enables a single follower robot (the "photographer") to quickly re-establish visual con- tact with a moving target (the "subject") that has escaped the follower’s field of view. Our work addresses this unavoidable scenario, which reactive controllers are typically ill-equipped to handle, by making intelligent predictions about the long- and short-term behavior of the target, and planning pursuit paths that will maximize the chance of seeing the target again. At the core of our pursuit method is the use of predictive models of target behavior, which help narrow down the possible future locations of the target to a few discrete hypotheses, as well as the use of combinatorial search in physical space to check those hypotheses efficiently. We model target behavior in terms of a learned navigation reward function, using Inverse Reinforcement Learning, based on semantic terrain features of satellite maps. Our pursuit algorithm continuously predicts the latent destination of the target, and its position in the future, and relies on efficient graph representation and search methods in order to navigate to location hypotheses at which the target is most likely to be seen at an anticipated time. We perform extensive evaluation of our predictive pursuit algorithm over multiple satellite maps, under thousands of simulation scenarios, against state-of-the art MDP and POMDP solvers, and we show that our method significantly outperforms them by exploiting domain-specific knowledge, while being able to run in real-time.