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One aspect of non-visual visualisation is providing accessibility to diagrams for users with visual impairments. In this paper, we review the literature on diagrams and non-visual presentation in order to elucidate the issues involved in making graph based diagrams accessible using speech and non-speech sound. First we examine the nature, scope and uses of these diagrams. We then describe the nature of diagrams: how do diagrams differ from other representations; how do sighted readers read, understand, and extract information from diagrams; what cognitive processes do diagrams facilitate; and what factors affect how diagrams may be understood? After a comparison of visual with aural presentation we discuss the work presented by others in this field, particularly looking at their reasons for implementing how they do in light of our examination of visual comprehension. The paper concludes with a discussion of how these issues combine and conflict to influence requirements for interface design.