A martini was an alcoholic beverage traditionally made from a mixture of gin and dry vermouth, with a variant "vodka martini" which substituted vodka for gin. Preparation of the martini generally consisted of a small amount of vermouth poured over ice to slightly melt and flavor the ice. The desired amount of gin or vodka was added, and the mixture was shaken or stirred according to taste and then served without the ice.
Philip Boyce, after arriving in Captain Christopher Pike's quarters in 2254 and putting ice into a glass to Pike's surpise, noted "who wants a warm martini?". When asked why he thought Pike needed one, Boyce commented, "Sometimes a man will tell his bartender things he'll never tell his doctor." (TOS: "The Cage", "The Menagerie, Part I")
L.Q. Clemonds ordered a martini, with two olives "for the vitamins", from the replicator of the USS Enterprise-D shortly after being awoken from a cryonics satellite in 2364. (TNG: "The Neutral Zone")