In this overview, commonly used dimensionality reduction techniques for data visualization and their properties are reviewed. Thereby, the focus lies on an intuitive understanding of the underlying mathematical principles rather than detailed algorithmic pipelines. Important mathematical properties of the technologies are summarized in the tabular form. The behavior of representative techniques is demonstrated for three benchmarks, followed by a short discussion on how to quantitatively evaluate these mappings. In addition, three currently active research topics are addressed: how to devise dimensionality reduction techniques for complex non‐vectorial data sets, how to easily shape dimensionality reduction techniques according to the users preferences, and how to device models that are suited for big data sets.WIREs Data Mining Knowl Discov2015, 5:51–73. doi: 10.1002/widm.1147This article is categorized under:Technologies > Machine LearningTechnologies > Structure Discovery and ClusteringTechnologies > Visualization