Wavelets have been on the forefront for more than three decades now. Wavelet transforms have had tremendous impact on the fields of signal processing, signal coding, estimation, pattern recognition, applied sciences, process systems engineering, econometrics, and medicine. Built on these transforms are powerful frameworks and novel techniques for solving a large class of theoretical and industrial problems. Wavelet transforms facilitate a multiscale framework for signal and system analysis. In a multiscale framework, the analyst can decompose signals into components at different resolutions followed by the application of the standard single-scale techniques to each of these components. In the area of process systems engineering, wavelets have become the de facto tool for signal compression, estimation, filtering, and identification. The field of wavelets is ever-growing with invaluable and innovative contributions from researchers worldwide. The purpose of this chapter is threefold: (i) to provide a semi-formal introduction to wavelet transforms for engineers; (ii) to present an overview of their applications in process systems engineering, with specific attention to controller loop performance monitoring and empirical modeling; and (iii) to introduce the ideas of consistent prediction-based multiscale identification. Case studies and examples are used to demonstrate the concepts and developments in this work. © 2013 Elsevier Inc.