The Subbasement is the training and research center, as well as the main base of operations, for the X-Men. It is located on the lower levels of the X-Mansion.
Prior to X-Men: First Class
With the advent of the nuclear age, Charles Xavier's stepfather became very concerned about the likelihood of a nuclear war breaking out. To insure his family's safety and protection, he had an underground bunker built under the Xavier Mansion to withstand the force and destruction of a nuclear explosion.
In 1962, with the break-up of Division X following the Hellfire Club's assault on the CIA's Covert Research Base, Xavier offered the use of his family's home as a training ground for the remaining members of the Division.
The underground bunker was used by Xavier to train Alex Summers due to the instability of Summers' power. Although set on fire at one point, the bunker remained intact, and it continued to serve as a training ground for Summers until he was able to get his powers under control.
Between X-Men: First Class and X-Men
The modern subbasement was planned and constructed around the time Xavier's School for Gifted Youngsters first opened in 1965. As evident in X-Men: Days of Future Past, the only area in the subbasement that was apparently developed and in use around this time was Cerebro.
By the time of the events of X-Men, the subbasement was fully developed, with additional features such as the Danger Room, the X-Jet Hanger, a laboratory and a dressing room. The subbasement was off limits to the students of the School and was only used by Professor X and members of the X-Men.
Logan's first experience in the X-Mansion was in the subbasement's laboratory, where he was taken and cared for following Sabretooth's attack in Canada. Xavier later gives Logan a tour of the X-Mansion, including areas of the subbasement. Logan was later given a CT scan in the laboratory, which revealed his adamantium skeleton.
Mystique, disguised as Bobby Drake, infiltrates the subbasement and infects Cerebro with a toxin, which in turn affects and poisons Xavier later on. Senator Kelly, who was affected by Magneto's conversion machine, dies in the subbasement's laboratory.
The X-Men later take-off from the hanger in order to confront Magneto. After the battle on Liberty Island, both Logan and Professor X are recovering in the subbasement's laboratory.
After Jean Grey was unexpectedly discovered alive at Alkali Lake, she was brought back to the X-Mansion and was placed in the laboratory in a sedated state in order to prevent her Phoenix personality from coming to the forefront.
In 2010, Trask Industries occupied the X-Mansion and, ostensibly, secured the entire subbasement.
By 2023, Trask Industries still operated within the subbasement of the X-Mansion. Iceman, Magneto and Professor X fly to the X-Mansion so that Iceman and Magneto can rescue Rogue, who is being experimented on in the room that formerly held Cerebro. Shortly after rescuing Rogue, the trio are met with Sentinels approaching from all sides of the subbasement. In order to let Magneto bring Rogue safely to the X-Jet, Iceman holds off the Sentinels long enough for Magneto and Rogue to escape, sacrificing his life in the process.
After Logan convinces Charles Xavier not to use his power suppressing serum and to embrace being "Professor X", he takes Logan and Hank to the Sub-basement to use Cerebro. However, Charles winces in pain after using it shortly, causing Hank to go check the wires. Logan realizes it's not the machinery, and prompts Charles to not lose hope. In order to help Charles, Logan tells Charles to scan his brain; Charles does so, experiencing all of the pain and loss Logan went through. Not able to deal with more pain and struggling, Charles attempts to turn back and give up. Logan, however, tells Charles to go past the pain and continue to go through his mind; in doing so, the 1973 Charles manages to get through Logan's mind, and ends up in the room where Logan's body is resting. The Charles Xavier of 2023, who is watching over Logan's body, notices the new mental presence in the room, recognizing it of that of his former self. The older Charles has a discussion with the younger Charles, and the younger Charles' hope for the future and benefit on mankind is rejuvenated. Filled with hope once more, Charles manages to use Cerebro successfully.
After Mystique finds out that Magneto's family was killed, she decides to help him. Having nowhere else to turn, she returns to her old home - the X-Mansion - in order to enlist the help of Charles Xavier. Xavier and Mystique than head down to the Sub-basement along with Moira MacTaggert, Alexander Summers, and Hank McCoy, Using Cerebro, Xavier locates Magneto along with Apocalypse and his other three Horsemen; Apocalypse notices that Magneto's mind is connected to Xavier's, and takes over Magneto's mind in order to control Xavier's. As Xavier is plugged into Cerebro, Apocalypse uses Cerebro to control the minds of every human in charge of each country's nuclear arsenal and has them fire their nukes into outer space. As his mind is linked to Xavier's, Xavier is able to see Apocalypse's goal of near-global extinction. Xavier tells Summers to wreak havoc, and Havok destroys Cerebro, thereby breaking the connections. However, the process leaves Xavier unconscious. Apocalypse and his Four Horsemen then teleport inside the sub-basement, and kidnap Xavier. In an attempt to stop the, Havok fires a powerful plasma energy beam; however, they teleport away and the beam hits a generator, destroying the entire mansion, including the sub-basement. With the exception of Havok, every other resident of the X-Mansion is saved by the quick-thinking heroics of Quicksilver.
The sub-basement was presumably rebuilt sometime after Magneto and Jean Grey rebuilt the mansion.