The Tarpeian Rock (//; Latin: Rupes Tarpeia or Saxum Tarpeium, Italian Rupe Tarpea) was a steep cliff of the southern summit of the Capitoline Hill, overlooking the Roman Forum in Ancient Rome. It was used during the Roman Republic as an execution site. Murderers, traitors, perjurors, and larcenous slaves, if convicted by the quaestores parricidii, were flung from the cliff to their deaths, as were the disabled and mentally ill.  The cliff was about 25 meters (80 ft) tall.
According to early Roman histories, when the Sabine ruler Titus Tatius attacked Rome after the Rape of the Sabines (8th century BC), the Vestal Virgin Tarpeia, daughter of Spurius Tarpeius, governor of the citadel on the Capitoline Hill, betrayed the Romans by opening the city gates for the Sabines in return for 'what they bore on their arms.' Titus Tatius bribed Tarpeia into letting his army into the gates in exchange for the golden bracelets and bejeweled rings. In Book 1 of Livy’s Ab Urbe Condita, the Sabines “accepti (in arcem) obtruam armis necavere,” meaning, “having been accepted into the citadel, [the Sabines] killed her, having been overwhelmed by weapons, and “scuta congesta”, meaning, “[they] heaped up shields [on her].” The Sabines crushed her to death with their shields, and her body was buried in the rock that now bears her name. Regardless of whether or not Tarpeia was buried in the rock itself, it is significant that the rock was named for her deceit. 
About 500 BC, Lucius Tarquinius Superbus, the seventh legendary king of Rome, leveled the top of the rock, removing the shrines built by the Sabines, and built the Temple of Jupiter Capitolinus on the intermontium — the area between the two summits of the hill. The rock itself survived this remodelling, being used for executions well into Sulla's time (early 1st century BC).
Note the Latin phrase, Arx tarpeia Capitoli proxima, which translates to, “the Tarpeian Rock is close to the Capitol,” which some have interpreted to mean that “one's fall from grace can come swiftly”.
To be hurled off the Tarpeian Rock was, in some sense, a fate worse than death, because it carried with it a stigma of shame. The standard method of execution in ancient Rome was by strangulation in the Tullianum. Rather, the rock was reserved for the most notorious traitors, and as a place of unofficial, extra-legal executions (for example, the near-execution of then-Senator Gaius Marcius Coriolanus by a mob whipped into frenzy by a tribune of the plebs).
Victims of this punishment included:
- Marcus Manlius Capitolinus, 384 BC, for sedition
- rebels from Tarentum, 212 BC
- Lucius Cornelius Chrysogonus, 80 BC
- Sextus Marius, 33 AD
- Simon bar Giora, 70 AD
- Platner (1929). A Topographical Dictionary of Ancient Rome, Tarpeius Mons, pp509-510. London. Oxford University Press.
- Lemprière, John (1827). A Classical Dictionary. E. Duychinck, Collin & co. p. 797. Retrieved 17 December 2010.
- Livy. Ab Urbe Condita. Macmillan Education Ltd. p. 20. ISBN 0 86292 296 8.
- Pseudo-Plutarch. Parallela Graeca et Romana. (Authorship disputed) (Loeb ed.).
Tarpeia, one of the maidens of honourable estate, was the guardian of the Capitol when the Romans were warring against the Sabines. She promised Tatius that she would give him entry to the Tarpeian Rock if she received as pay the necklaces that the Sabines wore for adornment. The Sabines understood the import and buried her alive. So Aristeides the Milesian in his Italian History.
- Plutarch. Lives - Sylla. trans. Joseph Dryden.
And afterwards, when he had seized the power into his hands, and was putting many to death, a freedman, suspected of having concealed one of the proscribed, and for that reason sentenced to be thrown down the Tarpeian rock, in a reproachful way recounted how they had lived long together under the same roof, himself for the upper rooms paying two thousand sesterces, and Sylla for the lower three thousand; so that the difference between their fortunes then was no more than one thousand sesterces, equivalent in Attic coin to two hundred and fifty drachmas.
- Plutarch. Lives - Coriolanus. trans. Joseph Dryden.
But, when, instead of the submissive and deprecatory language expected from him, he began to use not only an offensive kind of freedom, seeming rather to accuse than apologize, but, as well by the tone of his voice as the air of his countenance, displayed a security that was not far from disdain and contempt of them, the whole multitude then became angry, and gave evident signs of impatience and disgust; and Sicinnius, the most violent of the tribunes, after a little private conference with his colleagues, proceeded solemnly to pronounce before them all, that Marcius was condemned to die by the tribunes of the people, and bid the Aediles take him to the Tarpeian rock, and without delay throw him headlong from the precipice....Sicinnius then, after a little pause, turning to the patricians, demanded what their meaning was, thus forcibly to rescue Marcius out of the people's hands, as they were going to punish him; when it was replied by them, on the other side, and the question put, "Rather, how came it into your minds, and what is it you design, thus to drag one of the worthiest men of Rome, without trial, to a barbarous and illegal execution?"
- Plutarch, Lives; Livy, Ab Urbe Condita; M. Grant, Roman Myths.
- Livy. Book 6 [20.9]