The Vault was established sometime in 1874 and installed at St Luke's University. The Doctor's aim was to capture his past and future incarnations in order to have a giant orgy with his other selves. This plan fell through, however, when The Twelfth Doctor realised he had erectile dysfunction, brought on by persistent wanks over Clara and late night shenanigans with Nardole.
The Vault was later re-purposed with containing Missy, whom he captured during his vacation on Skaro. The Doctor visits Missy in the vault every week, bringing a new toy with him everytime. After the Monks gave him a blowjob to cure his erectile dysfunction, his intimacy with Missy went to the next level. Eventually his antics were discovered by UNIT and he was charged with false imprisonment and rape. Some say the sex was so intense, The Master went through twenty six incarnations over the course of 2 weeks, most of which were black men.