Internet advertising is a fast growing business which has proved to be significantly important in digital economics. It is vitally important for both web search engines and online content providers and publishers because web advertising provides them with major sources of revenue. Its presence is increasingly important for the whole media industry due to the influence of the Web. For advertisers, it is a smarter alternative to traditional marketing media such as TVs and newspapers. As the web evolves and data collection continues, the design of methods for more targeted, interactive, and friendly advertising may have a major impact on the way our digital economy evolves, and to aid societal development. Towards this goal mathematically well-grounded Computational Advertising methods are becoming necessary and will continue to develop as a fundamental tool towards the Web. As a vibrant new discipline, Internet advertising requires effort from different research domains including Information Retrieval, Machine Learning, Data Mining and Analytic, Statistics, Economics, and even Psychology to predict and understand user behaviours. In this paper, we provide a comprehensive survey on Internet advertising, discussing and classifying the research issues, identifying the recent technologies, and suggesting its future directions. To have a comprehensive picture, we first start with a brief history, introduction, and classification of the industry and present a schematic view of the new advertising ecosystem. We then introduce four major participants, namely advertisers, online publishers, ad exchanges and web users; and through analysing and discussing the major research problems and existing solutions from their perspectives respectively, we discover and aggregate the fundamental problems that characterise the newly-formed research field and capture its potential future prospects.