The methods of trapping and cooling of atoms and ions have been transformative for atomic clocks due to the reduction, and in some cases elimination, of major systematic frequency shifts. Continuously operating atomic clocks based on trapped mercury ions have existed for decades but until recently have been restricted to terrestrial applications. The recently completed Deep Space Atomic Clock (DSAC) mission demonstrated the first trapped ion clock operation in space. Here we review DSAC as well as follow-on improvements towards the realization of high stability, long life Hg ion atomic clocks for foreseen ground and flight application.