Legend has it that it's made out of green cheese. Solomon Grundy was briefly exiled to the Moon after his second battle with Green Lantern (Alan Scott). More notably is the fact that the Justice League Watchtower was located here. The moon also became the base of operations for the deity known as Eclipso. The heroes of Earth once staged a massive assault against Eclipso's citadel - a fight that cost the life of Will Payton, aka, Starman. 
During the leading events to the World's End event during the events of Number of the Beast, the moon was heavily and partially destroyed and scattered into many pieces by a battle between The High and one of his rampant "Reaper" clones.
Points of Interest
In Superman #156, Superman, believing he is dying of Virus X exposure, uses his vision powers to leave an inspiring message on the Moon, which also reveals his secret identity.
Pre-Zero Hour, the Moon was destroyed in the 30th century by the Linear Man.