It is unknown how the van was first obtained, but Murray was very deeply connected to it. It was very useful in Sly Cooper and the Thievius Raccoonus, serving as the Gang's getaway vehicle. The Van had a satellite, and in The Cold Heart of Hate, it gained rooftop turrets to fire at Clockwerk's goons and a battering ram to smash computers and Fire Slugs. Both of these additions were from original designs by Otto van Cooper. The turret was damaged during the Gang's initial drive into Clockwerk's lair.
In Sly 2: Band of Thieves, the van is never used in actual gameplay but is always parked in the safehouse garage, ready as the getaway vehicle. At the end of The Predator Awakes, Bentley is forced to learn how to drive the van in order to escape the jungles of India and also to rescue his friends. It is used as the main transportation vehicle until the end of Menace from the North, eh!, when it is seen floating away on a piece of ice.
In Sly 3: Honor Among Thieves, the van is not mentioned until A Cold Alliance, when Penelope reads some strange signals coming from the bay. Reconnaissance showed the disturbance to be the team's long-lost van. With the help of both Penelope and the Panda King, Murray is able to haul his van back to the safe house where Sly Cooper and Bentley (with a little help from Inspector Carmelita Fox) recharge its batteries for the team's getaway. Later in the game, the core members use the Panda King's fireworks to launch the van up to the Cooper Vault to rescue the Cooper family fortune. After the Cooper Vault job, Murray takes the van and begins his career as a racecar driver, stock-van class.
In Sly Cooper: Thieves in Time, Bentley converts the van into a time machine. The time machine was first mentioned in the ending of Sly 3. Bentley infers that he wants to use the time machine to see what their future holds now that Sly has run off with Carmelita, Murray has joined the racing field, and Bentley and Penelope are the keepers of the improved Cooper Vault and the Thievius Raccoonus.
Between the events of Sly 3 and Thieves in Time, Murray continued his racing career, until he could no longer find a sponsor due to his high insurance premiums. Because of this, Murray headed into demolition derby, where he remained undefeated. He dropped everything when Bentley showed up and informed Murray that the van was an integral part of his plan to save Sly's family history from being erased forever.
The time machine is an essential part of the gang's plans in Thieves in Time, as it is used to travel back and forward through time to different periods where Sly's ancestors live, the mission being to restore the pages of the Thievius Raccoonus. The time machine uses carbon-dating to travel through time, using various artifacts to travel back to the specific time periods, including a Samurai Dagger to get to Feudal Japan, a Sheriff Badge to get to the Old West, Murray's Australian Fossil Necklace to get to the Ice Age, Grizz's Crown to get to Medieval England, a Gold Coin with a Jewel in the center to get to Ancient Arabia, and an Eiffel Tower Keychain to return to the present day. The hover boosters on the improved van also allow it to fly, as shown in "Timing is Everything." A side door has also been added to the van; this is used during "Operation: Gold Digger" when the Gang attempts to steal the gold from Toothpick's train.
It is unknown how the Van managed to store Clockwerk parts before heading to Canada since the size of the collected Clockwerk parts clearly did not fit the Van at Sly 2: Band of Thieves.
The van itself did not go many changes throughout the series and it is also unknown how Murray can repair the Van back into an operational state when crashed on 10,000 BC despite lacking of spare parts needed.
Surprisingly, the Van did not receive any rust or scratches considering between Sly 2: Band of Thieves and Sly 3: Honor among Thieves after drifting around the ocean years later to China.