The use of logic in Information Retrieval (IR) enables one to formulate models that are more general than other well known IR models. Indeed, some logical models are able to represent, within a uniform framework, various features of IR systems, such as hypermedia links, multimedia content, and users knowledge. Logic also provides a common approach to the integration of IR systems with logical database systems. Finally, logic makes it possible to reason about an IR model and its properties. This latter possibility is becoming increasingly important since conventional evaluation methods, although good indicators of the effectiveness of IR systems, often give results which cannot be predicted, or for that matter satisfactorily explained. However, logic by itself cannot fully model IR. In determining the relevance of a document to a query the truth value or the validity of a logical formula relating the two is not enough. It is necessary to take into account the uncertainty inherent in such a formulation. This paper gives an overview of how past and current research have combined the use of logical and uncertainty theories for the formulation of more advanced models for the representation and retrieval of information.