The development of a given discipline in science and technology often depends on the availability of theories capable of describing the processes which control the field and of modelling the interactions between these processes. The absence of an accepted theory of information retrieval has been blamed for the relative disorder and the lack of technical advances in the area. The main mathematical approaches to information retrieval are examined in this study, including both algebraic and probabilistic models, and the difficulties which impede the formalization of information retrieval processes are described. A number of developments are covered where new theoretical understandings have directly led to the improvement of retrieval techniques and operations.