Mining high-dimensional data streams poses a fundamental challenge to machine learning as the presence of high numbers of attributes can remarkably degrade any mining task's performance. In the past several years, dimension reduction (DR) approaches have been successfully applied for different purposes (e.g., visualization). Due to their high-computational costs and numerous passes over large data, these approaches pose a hindrance when processing infinite data streams that are potentially high-dimensional. The latter increases the resource-usage of algorithms that could suffer from the curse of dimensionality. To cope with these issues, some techniques for incremental DR have been proposed. In this paper, we provide a survey on reduction approaches designed to handle data streams and highlight the key benefits of using these approaches for stream mining algorithms.