  The dynamics of magnetic moments consist of a precession around the magnetic
field direction and a relaxation towards the field to minimize the energy.
While the magnetic moment and the angular momentum are conventionally assumed
to be parallel to each other, at ultrafast time scales their directions become
separated due to inertial effects. The inertial dynamics give rise to
additional high-frequency modes in the excitation spectrum of magnetic
materials. Here, we review the recent theoretical and experimental advances in
this emerging topic and discuss the open challenges and opportunities in the
detection and the potential applications of inertial spin dynamics.
