Online advertising, the pillar of the “free” content on the Web, has revolutionized the marketing business in recent years by creating a myriad of new opportunities for advertisers to reach potential customers. The current advertising model builds upon an intricate infrastructure composed of a variety of intermediary entities and technologies whose main aim is to deliver personalized ads. For this purpose, a wealth of user data is collected, aggregated, processed and traded behind the scenes at an unprecedented rate. Despite the enormous value of online advertising, however, the intrusiveness and ubiquity of these practices prompt serious privacy concerns. This article surveys the online advertising infrastructure and its supporting technologies, and presents a thorough overview of the underlying privacy risks and the solutions that may mitigate them. We first analyze the threats and potential privacy attackers in this scenario of online advertising. In particular, we examine the main components of the advertising infrastructure in terms of tracking capabilities, data collection, aggregation level and privacy risk, and overview the tracking and data-sharing technologies employed by these components. Then, we conduct a comprehensive survey of the most relevant privacy mechanisms, and classify and compare them on the basis of their privacy guarantees and impact on the Web.