In this talk, we address inverse problems in imaging unknown targets from far-field measurement data. In the first part, we discuss sampling methods, which recover targets by constructing indicator functions that peak at their locations. We analyze the behavior of these functions under various measurement configurations. In the second part, we turn to the problem of tracking moving targets. In particular, we show how a Bayesian optimization framework can be combined with the analytic properties of far-field data to determine the position and orientation of a moving scatterer.