This paper follows a formal approach to information retrieval based on statistical language models. By introducing some simple reformulations of the basic language modeling approach we introduce the notion of importance of a query term. The importance of a query term is an unknown parameter that explicitly models which of the query terms are generated from the relevant documents (the important terms), and which are not (the unimportant terms). The new language modeling approach is shown to explain a number of practical facts of today's information retrieval systems that are not very well explained by the current state of information retrieval theory, including stop words, mandatory terms, coordination level ranking and retrieval using phrases. Categories and Subject Descriptors H.3.3 [Information Storage and Retrieval]: Information Search and Retrieval General Terms Theory Keywords Information Retrieval, Formal Models, Language Models, Search Strategies