There are many variations of a Martini and sometimes itâ€™s easy to feel overwhelmed by the choice. With these tips, however, you will quickly sound like an expert, exploring the different versions of the classic cocktail and finding the most appealing version that suits you. Firstly, the original Martini was, and still is, made with gin. If you want a Martini made with vodka you need to ask for Vodkatini or a Vodka Martini. Back in the 1950s in the â€œMad Menâ€?