This talk will first give a selective introduction to visualization tools for multivariate data. These tools will allow us to "see" complex quantitative dependences with high-dimensional data projections. The goal will be to demystify the idea of "seeing" in high-dimensional spaces. The main part of the talk will describe the combination of data visualization and multidimensional scaling (MDS). MDS is a method for visualizing proximity data, that is, data where objects are characterized by dissimilarity values for all pairs of objects. MDS constructs maps of these objects in Euclidean spaces by interpreting the dissimilarities as distances. We show applications of MDS to the mapping of computer usage data, to the dimension reduction of marketing segmentation data, to the layout of mathematical graphs and social network graphs, and finally to the reconstruction of molecules in nano technology. MDS in its conventional batch implementations is prone to uncertainties with regard to 1) local minima in the underlying optimization, 2) sensitivity to the choice of the optimization criterion, 3) artifacts in point configurations, and 4) local inadequacy of the point configurations. These uncertainties will be addressed by a set of interactive graphical tools. While this may seem like a low brow approach to serious analytical difficulties, it in fact satisfies a user's curiosity better than analytical approaches.