We present results for the relation between a heavy quark mass defined in the on-shell and M̅S̅ scheme to four-loop order. The method to compute the four-loop on-shell integral is briefly described and the new results are used to establish relations between various short-distance masses and the M̅S̅ quark mass to next-to-next-to-next-to-leading order accuracy. These relations play an important role in the accurate determination of the M̅S̅ heavy quark masses.