Although named after the emperor Tiberius, this palace was not built by him; Tiberius was somewhat paranoid about his lack of popularity and disliked Rome, so he chose to spend most of his reign living in his villa on Capri. The elaborate structure that came to be known as the Domus Tiberiana was quite possibly constructed by the emperor Claudius (son of Tiberius's brother Drusus) after Claudius's marriage to Agrippina. At any rate, the very high podium and elaborate substructures of this building closely resemble those of the temple Agrippina began to erect after her husband's death, the Temple of the Deified Claudius in Region II.
In the substructures of this palace are many small rooms that were probably occupied by slaves and soldiers when this was used as the imperial residence, before Domitian constructed the grandiose Palatium next door. Unsurprisingly, the men who spent time in those small rooms amused themselves by writing graffiti on the walls, including this caricature of the emperor Nero, signed by "Tullius Romanus, soldier."
This building has an underground passage called a cryptoporticus; if you descend the stairs you will learn what significant historical event occurred there.