  I review the structure of the leading infrared renormalon divergence of the
relation between the pole mass and the $\overline{\rm MS}$ mass of a heavy
quark, with applications to the top, bottom and charm quark. That the pole
quark mass definition must be abandoned in precision computations is a
well-known consequence of the rapidly diverging series. The definitions and
physics motivations of several leading renormalon-free, short-distance mass
definitions suitable for processes involving nearly on-shell heavy quarks are
discussed.
