Historically, fortified wines originated in Europe, and they have in common a high alcohol content to increase their shelf-life during long journeys to northern Europe and the American continent. Nowadays, the world’s better-known Marsala, Port, Sherry, and Vermouth due to their high alcoholic content, sweet taste, and intense aromatic profile, are designated as dessert wines and sometimes served as aperitifs. This review gives an overview of the traditional vinification process, including the microbiota and autochthonous yeast, the use of aromatic botanicals, and regulatory aspects of the main Italian, Portuguese, and Spanish fortified wines. The wine-making process is essential to defining the volatile organic compounds (VOCs) that characterize the aroma of each fortified wine, giving them an organoleptic fingerprint and “terroir” characteristics. The various volatile and odorous compounds found in fortified wines during oxidative and thermal aging are discussed in the last part of this review.