  Recent developments in frequency metrology and optical clocks have been based
on electronic transitions in atoms and singly charged ions as references. These
systems have enabled relative frequency uncertainties at a level of a few parts
in $10^{-18}$. This accomplishment not only allows for extremely accurate time
and frequency measurements, but also to probe our understanding of fundamental
physics, such as variation of fundamental constants, violation of the local
Lorentz invariance, and forces beyond the Standard Model of Physics. In
addition, novel clocks are driving the development of sophisticated technical
applications. Crucial for applications of clocks in fundamental physics are a
high sensitivity to effects beyond the Standard Model and Einstein's Theory of
Relativity and a small frequency uncertainty of the clock. Highly charged ions
offer both. They have been proposed as highly accurate clocks, since they
possess optical transitions which can be extremely narrow and less sensitive to
external perturbations compared to current atomic clock species. The selection
of highly charged ions in different charge states offers narrow transitions
that are among the most sensitive ones for a change in the fine-structure
constant and the electron-to-proton mass ratio, as well as other new physics
effects. Recent advances in trapping and sympathetic cooling of highly charged
ions will in the future enable high accuracy optical spectroscopy. Progress in
calculating the properties of selected highly charged ions has allowed the
evaluation of systematic shifts and the prediction of the sensitivity to the
"new physics" effects. This article reviews the current status of theory and
experiment in the field.
