The Tantalus colony was a Federation penal colony located on planet Tantalus V in the 23rd century. Violent criminals from all over the Federation were sent there for rehabilitation. Like all penal colonies in the Federation, it was protected by a force field that prevented any transporter activity, until the field was de-activated. Therefore, any vessel that needed access to the colony had to contact the facility and supply the correct documentation for access.
In 2266, the facility was under the operational control of Dr. Tristan Adams. While initially praised for transforming the prison system in the Federation, it was discovered by the crew of the USS Enterprise that Adams were subjecting inmates and staff to the experimental neural neutralizer device, which would affect their brain-patterns. After the Enterprise put a stop to these illegal experiments, Adams' assistant, Dr. Simon Van Gelder, was placed in charge of the colony. (TOS episode: "Dagger of the Mind")
In 2265, Captain James T. Kirk joked with Lieutenant Commander Gary Mitchell that he could visit him at the penal colony on Tantalus V should he be discovered smuggling a bottle of Saurian brandy into the Enterprise's sickbay after Mitchell was hit by a poison dart on the planet Dimorus. (TOS - My Brother's Keeper novel: Enterprise)