Computational advertising is an emerging scientific sub-discipline, at the intersection of large scale search and text analysis, information retrieval, statistical modeling, machine learning, classification, optimization, and microeconomics. The central challenge of computational advertising is to find the "best match" between a given user in a given context and a suitable advertisement. The aim of this tutorial is to present the state of the art in Computational Advertising, in particular in its IR-related aspects, and to expose the participants to the current research challenges in this field. The tutorial does not assume any prior knowledge of Web advertising, and will begin with a comprehensive background survey. Going deeper, our focus will be on using a textual representation of the user context to retrieve relevant ads. At first approximation, this process can be reduced to a conventional setup by constructing a query that describes the user context and executing the query against a large inverted index of ads. We show how to augment this approach using query expansion and text classification techniques tuned for the ad-retrieval problem. In particular, we show how to use the Web as a repository of query-specific knowledge and use the Web search results retrieved by the query as a form of a relevance feedback and query expansion. We also present solutions that go beyond the conventional bag of words indexing by constructing additional features using a large external taxonomy and a lexicon of named entities obtained by analyzing the entire Web as a corpus. The last part of the tutorial will be devoted to a potpourri of recent research results and open problems inspired by Computational Advertising challenges in text summarization, natural language generation, named entity recognition, computer-human interaction, and other SIGIR-relevant areas.