We have illustrated the utility of WTs throughout this chapter, for cleaning, smoothing, and denoising data, as well as the benefits of their direct use as molecular property descriptors. It is clear from the examples cited that this versatile technology can identify and quantify important features within spectra or property distributions of chemical interest for use in both classification and regression models, to achieve near-linear scaling in electronic structure calculations and serve to control the quality of a basis set in ab initio molecular dynamics simulations. The evolution of wavelets in chemistry parallels the development of ever more sophisticated computational methods and hardware performance. In a relatively short period of time, wavelet methods have grown in importance from a noise filter and baseline correction tool to a fundamental component of modern data analysis, computational chemistry, and knowledge discovery. Copyright © 2006 Wiley-VCH, John Wiley & Sons, Inc.