The martini came about in the eighteen fifties and got its name from either the Occidental Hotel in San Francisco, or was named after the vermouth company, Martini. The glass was already used for other drinks until the Martini was invented.
The conical bowl was designed to expose the drink to the air and so the olives would stand upright. The long stem was made so that warm hands would not affect the temperature of the drink. Six different models available at franmara.com. 8127, 8128, 8622, 8505, 8526, 8622.