Explore the application of Partial Least Squares (PLS) in nonlinear regression through this 32-minute conference talk by R. Dennis Cook from the University of Minnesota. Delve into the limitations of standard PLS regression algorithms like NIPALS and SIMPLS for nonlinear relationships between response and predictors. Discover how envelope theory challenges conventional wisdom, revealing that the dimension reduction aspect of these algorithms remains effective even in nonlinear scenarios. Examine the implications for existing nonlinear PLS-like methods and their utility. Follow the presentation's structure, covering the introduction, historical context, PLS algorithm mechanics, key findings, linear PLS, crucial factors, proposed methodologies, comparisons, Decatur data analysis, neural network applications, and concluding remarks. Gain insights into the potential consequences of these findings for the field of chemometrics and machine learning.