The Vanishing Point is a place located outside of time. It was utilized by the Time Masters as base of operations. Supposedly, it was the only location not affected by the Oculus device. The Vanishing Point was also the location of the Oculus Wellspring, before its ultimate destruction at the hands of Leonard Snart.
Rip Hunter and Miranda Coburn awaited trial before the Time Masters Council due to breaking their rule of having a relationship. However, the latter agreed to leave the Time Masters, allowing Rip to walk free.
After Vandal Savage had taken over the world in 2166, Rip Hunter went before the Time Masters Council, hoping to form a team. They refused approval, instead forcing him to go rogue and create a team of his own.
After Leonard Snart left Mick Rory stranded in the timeline, he was trained by the Time Masters to deal with Rip Hunter's team. He spent a lot of time there, until he was ready and was sent to eliminate them, although he was only able to capture Snart.
Rip Hunter's team captured Vandal Savage and took him to the Vanishing Point, hoping to have him incarcerated for messing around with time. However, the Time Masters revealed themselves to be allied with Savage and went to arrest all of Hunter's team, save for Sara Lance and Leonard Snart, who evaded capture by hiding in the Waverider's vents, and Jefferson Jackson, who was sent back to 2016 in the jumpship to be cured of his temporal radiation poisoning.
With Sara and Snart on the loose, the Time Masters had no choice but to keep Rip and the others alive for the time being. While Mick was being conditioned into becoming Chronos again, Druce revealed to Rip that in 2175, Earth would be invaded by the Thanagarians and if Savage did not unite the world to repel them, even the Vanishing Point would fall to the invaders. He then showed Rip the Oculus, a device that allowed the Time Masters to predict and manipulate timeline, controlling the actions of Rip's team that would work in favour of Savage. Being outside time, the Vanishing Point was the only place in space and time free from the device's influence.
Sara and Snart managed to sabotage the Time Master's time fleet by infecting their AIs with a virus created by Gideon before rescuing Rip and the others. Mick managed to overcome his brainwashing and fulfilled his promise of killing Time Master Declan. The Vanishing Point then attempted to thwart their escape by catching the Waverider in a tractor beam, only for Ray Palmer to use Mick's gauntlet to override the command.
Rip's team then targeted the Oculus Wellspring to prevent the Time Masters from manipulating the timeline any further. Druce came with a platoon to stop and execute them, only to be caught off guard by Jax in the jumpship. Eventually, they discovered the Oculus had to be destroyed manually, and Snart stayed behind to destroy the Oculus, resulting in the destruction of the Vanishing Point and his inevitable death. 
It was later revealed by Rip Hunter that the Legion of Doom had been using the Vanishing Point as a hideout.
DC's Legends of Tomorrow