The martini is a cocktail traditionally made with gin and dry white vermouth. The ratio varies greatly depending on who you talk to, from 2:1 (2 parts gin, 1 part vermouth) to a 15:1 ratio, or even using an atomizer for a light spray of vermouth.
Replacing gin with vodka has now become so common that many don't associate a martini with gin. With martini bars found everywhere, the martini has arguably become the most well-known mixed alcoholic beverage. It's a bit like the spread of the English language around the world, everyone speaks it, but few do it correctly.