In this chapter, we will first look at the motivations for us to do dimension reduction of the data, including feature extraction and visualization. Then, a good range of different approaches are introduced, from traditional statistical methods such as principal component analysis and multi-dimension scaling to kernel methods, neural network implementations, and modern visualization techniques such as Isomap and t-SNE. Again, different metrics for assessing distance or dissimilarity between data points play instrumental roles in the relevant algorithmic establishments.