We review the current status of flavor-changing neutral currents in the charm sector. We focus on the standard-model predictions and identify the main sources of theoretical uncertainties in both charm mixing and rare charm decays. The potential of these observables for constraining short-distance physics in the standard model and its extensions is compromised by the presence of large nonperturbative effects. We examine the possible discovery windows in which short-distance physics can be tested and study the effects of various extensions of the standard model. The current experimental situation and future prospects are reviewed.