This special issue describes several approaches to semantic knowledge representations. Each approach relies on statistical procedures to derive or analyze its representation. The articles cover a variety of statistical techniques which capture different aspects of knowledge representation. These techniques include using high-dimensional semantic spaces for representing word and passage meaning, Knowledge Diagraph Contribution (KDC) analysis for comparing propositional representations, and Principal Components Analysis and Singular Value Decomposition for determining the primary semantic relationships among concepts. Although the representations described primarily represent semantic information, some approaches incorporate syntactic information as well, most particularly the KDC analysis and the HAL high-dimensional space model. All of the statistical approaches in this issue capture the effects of regularities inherent in language. These regularities are derived either through how words occur in similar contexts, such as sentences or paragraphs, or through semantic relationships among concepts or propositions in a text or reader"s representation. With the development of powerful computers, computational methods, and collections of large corpora in electronic form, new statistical approaches to text and discourse have become possible. Many of these approaches have focused on analyzing at levels such as word recognition, syntactic processing, and formal semantics. However, the approaches in this issue tend to focus on semantic and higher-level features of discourse and to test their representations against subjects" representations of discourse derived from empirical data. While these approaches can serve as practical tools for the analysis of texts and readers" recall, they also serve as theoretical approaches to knowledge representation. They address issues such as the derivation of meaning of words and text passages based on context and the determination of the representation of the primary associations between concepts or propositions. Accordingly, the articles have implications for the extension of existing theories and the development of new theories of semantic knowledge representation. The articles in this issue describe approaches that should be of use to the Discourse Processes community. These approaches can serve as practical applications to analyze texts and summaries, predict learning, test models, and develop training material. They can also help inform theory on knowledge representations in discourse. As theory, these articles address issues of the role of context, knowledge structures, and discourse structures for understanding the representation of semantic information presented in texts and formed by readers.