Grayson's Clinic was owned by the Gilberts, which they obtained near the end of the Civil War, after all of the vampires in town were thought to have been killed in a fire. The Founding Families of Mystic Falls divided up the property and possessions of the vampires. It was previously an apothecary known to be owned by Pearl, and the building is one of the original structures in Mystic Falls. Grayson Gilbert operated his medical practice out of the building until he died; it can be assumed that this is where Isobel gave birth to Elena. The building was inherited by Jeremy and Elena, but Jenna had control of it until they turned 18.
Throughout The Vampire Diaries Series
Jenna met with Pearl shortly after she was released from the tomb, and was planning on renting it out to her, who planned to open her apothecary again. Once John Gilbert returned to Mystic Falls, he told Jenna that since Elena and Jeremy are minors, and since he was the estate's trustee, he gets the final say on the building.
Later on, members of The Founder's Council met there to discuss their plan to use the Gilbert Device on the vampires in Mystic Falls. John Gilbert used it as a central point for activating The Device. This building is also where they planned to bring the vampires after the device was activated. They could see who was a vampire by who fell to the ground in pain at the sound the device made, and those who were identified as vampires were injected with vervain and put in the basement, where they planned to start a fire to kill them for good. John staked Anna right before he set the basement on fire, killing what was probably the rest of the tomb vampires. Since the device had also incapacitated Mayor Richard Lockwood, he was incorrectly thought to be a vampire and put in the basement as well. He was soon killed by another vampire before he could be burnt alive in the fire.
Damon Salvatore was also trapped in the fire, but with the help of Bonnie, Stefan was able to save him. The fire was covered up, with the excuse that the fire was caused by faulty wiring in the building.
Wes kept Elena in here. The building is almost destroyed by the fire. We learn that the building is an Augustine lab and that the building has been unoccupied since the fire 2010.
Throughout The Originals Series
The Vampire Diaries