One of the most important primitive data types in modern data processing is text. Text data are known to have a variety of inconsistencies (e.g., spelling mistakes and representational variations). For that reason, there exists a large body of literature related to approximate processing of text. This monograph focuses specifically on the problem of approximate string matching, where, given a set of strings S and a query string υ, the goal is to find all strings s ∈ S that have a user specified degree of similarity to υ. Set S could be, for example, a corpus of documents, a set of web pages, or an attribute of a relational table. The similarity between strings is always defined with respect to a similarity function that is chosen based on the characteristics of the data and application at hand. This work presents a survey of indexing techniques and algorithms specifically designed for approximate string matching. We concentrate on inverted indexes, filtering techniques, and tree data structures that can be used to evaluate a variety of set based and edit based similarity functions. We focus on all-match and top-k flavors of selection and join queries, and discuss the applicability, advantages and disadvantages of each technique for every query type.