We study the expressiveness and performance of full-text search languages. Our main motivation is to provide a formal basis for comparing such languages and todevelop a model for full-text search that can be tightly integrated withstructured search. We develop a formal model for full-text search based on thepositions of tokens (words) in the input text, and develop a full-text calculus(FTC) and a full-text algebra (FTA) with equivalent expressive power. Thissuggests a notion of completeness for full-text search languages and can be usedas a basis for a study of their expressiveness. We show that existing full-textlanguages are incomplete and develop {\tt COMP}, a complete full-text searchlanguage. We also identify practical subsets of {\tt COMP} that are morepowerful than existing languages, develop efficient query evaluation algorithmsfor these subsets, and study experimentally their performance.