Mixing and $CP$ violation in the charm system

In recent years charm physics has undergone a renaissance, one which has been catalysed by an unexpected and impressive set of experimental results from the $B$-factories, the Tevatron and LHCb. The existence of $D^0\bar{D}{}^0$ oscillations is now well established, and the recent discovery of $CP$ violation in $D^0$ decays has further renewed interest in the charm sector. In this article we review the current status of charm-mixing and $CP$-violation measurements, and assess their agreement with theoretical predictions within the Standard Model and beyond. We look forward to the great improvements in experimental precision that can be expected over the coming two decades, and the prospects for corresponding advances in theoretical understanding.