Projection pursuit is concerned with "interesting" projections of high dimensional data sets, with finding such projections by machine, and with using them for nonparametric fitting and other data-analytic purposes. This survey attempts to put the fascinating problems and ramifications of projection pursuit--which range from principal components, multidimensional scaling, factor analysis, nonparametric regression, density estimation and deconvolution of time series to computer tomography and problems in pure mathematics--into a coherent perspective