The medal is similar to Payback from many other games.
The Revenge medal was redesigned between the Halo: Reach Beta and the final release. Originally it was similar to the final "Reload This!" medal; after the redesign it resembled "Death from the Grave " medal, but instead, the medal is yellow instead of white and has a mouth.
In Halo 4 the medal is additionally imposed on a blue circle and grey cross.