Commandeered by Captain Glory of The 18th Kree Diplomatic Gestalt, The Marvel was sent on a mission to negotiate The Kree/Skrull Ceasefire and ended millennia of cosmic hostility and war. On its return trip to Hala, the Marvel received distress calls from five doomed civilizations.
Upon arriving to discover the source of the distress calls, The Marvel and its crew ran afoul of three Astro-Gods from The First Firmament who were in the process of recharging their immense "sink-suits", which required the power of gravity refraction and epic genocide in order to allow The Astro-Gods access to a higher plane of existence called "The Hypoverse."
The stress being caused to the fabric of reality by their inhumane actions caused the scaffolding of time and space to rupture and collapse, as a result The Marvel ended up stranded on the far side of The Omniverse within "The Unfinished Universe."
It was there that a crewman named Doc Wonder sacrificed his life to give The Kirby Machines the power and ability to venture through The Omniverse as if it were normal space.
After traversing nearly ten billion alternate realities, parallel universe and divergent timelines such as The Wildstorm Universe, The Marvel and its crew came within one reality of reaching home. But as The Marvel passed through Earth-616, it was shot down by The Midas Corporation and ended up stranded in the Mainstream Marvel Universe.
Everyone, save for Ensign Marvel (Noh-Varr), the ship's computer core Plex and all of the entities imprisoned in "The Concept Dungeons" such as Hexus the Living Corporation and Idealus, The Fictional Man were killed when The Marvel was hit by a barrage of missiles.
The Marvel was taken into SHIELD custody shortly after Noh-Varr was apprehended by Dum Dum Dugan. Some time after Noh-Varr reclaims The Marvel and it is now in low earth orbit where he uses it as his base.