Tal-Shaya was a method of execution performed by the ancient Vulcans. Tal-Shaya involved breaking the neck of an individual in a very precise method designed to cause instant death, and was in Vulcan's past to be considered a merciful form of execution.
In 2268 the Tellarite Ambassador Gav was murdered by an assassin who used Tal-Shaya to kill the Ambassador while being taken to a conference on the planet Babel to decide the question of the Coridan admission to the Federation. Spock was able to quickly identify the method of execution as Tal-Shaya, and revealed that Vulcans would know how to perform such an act. As a result, suspicion fell to Sarek, also being taken on board the USS Enterprise to Babel. It was later revealed that an Orion agent on board the Enterprise had killed Gav. (TOS episode: "Journey to Babel")
In 2381, Spock considered performing tal-shaya on the Reman Angarraken, who had attempted to assassinate him, after he was able to repel the attack and render Angarraken unconscious. (ST - Typhon Pact novel: Rough Beasts of Empire)