Anna Fang built the airship when she was a slave in the junkyards of Arkangel, sneaking away bits and pieces and eventually assembling it in full. When the airship was complete, she escaped in it and began her life as an Anti-Tractionist spy, using her cover as a trader to spy on Traction Cities.
When Fang is killed at the end of Mortal Engines, Thomas Natsworthy and Hester Shaw "inherit" the Jenny, and start their own lives as traders. After two years, the Jenny is stolen by Nimrod Pennyroyal at the climax of Predator's Gold.
Pennyroyal later becomes the mayor of Brighton, and the Jenny Haniver is put on display as the ship he escaped from the Arctic in. At the climax of Infernal Devices, Tom and Hester steal it back and escape the city in it.
It then become a trading airship for Tom and his daughter Wren, and is used as their means of conveyance in the final book, A Darkling Plain. As they approach their final battle, they are attacked by Stalker birds, and the Jenny explodes and crashes.
The Jenny had souped up engines, and rocket defence pods. It was considerably faster and more maneueverable than it looked, as is proved in Predator's Gold when it escapes from Green Storm airships by flying through a traction city. The rocket pods remain empty after Mortal Engines, as Tom Natsworthy morally refuses to use them.