<p>The Lasso (least absolute shrinkage and selection operator) and Ridge regression are two fundamental regularization techniques in modern statistical learning. This paper provides a comprehensive review of these methods, focusing on their literature, theoretical underpinnings, practical differences, recent advancements, and diverse applications in machine learning, with additional insights from bioinformatics and finance. We discuss the historical development of Lasso and Ridge regression, compare their behaviours and performance, and describe extensions such as the Elastic Net, adaptive Lasso, and other improvements. An illustrative example with <Emphasis FontCategory="SansSerif">R</Emphasis> code is included to demonstrate the implementation of Lasso and Ridge in practice. Finally, we outline future research directions, highlighting ongoing developments and the continuing importance of Lasso and Ridge regression in high-dimensional data analysis.</p>