The article introduces the basic concepts of finite-state language processing: regular languages and relations, finite-state automata, and regular expressions. Many basic steps in language processing, ranging from tokenization, to phonological and morphological analysis, disambiguation, spelling correction, and shallow parsing, can be performed efficiently by means of finite-state transducers. The article discusses examples of finite-state languages and relations. Finite-state networks can represent only a subset of all possible languages and relations; that is, only some languages are finite-state languages. Furthermore, this article introduces two types of complex regular expressions that have many linguistic applications, restriction and replacement. Finally, the article discusses the properties of finite-state automata. The three important properties of networks are: that they are epsilon free, deterministic, and minimal. If a network encodes a regular language and if it is epsilon free, deterministic, and minimal, the network is guaranteed to be the best encoding for that language.