The article provides a comprehensive review of the random forest algorithm, a popular method for classification and regression tasks. Proposed by L. Breiman in 2001, random forests combine multiple randomized decision trees and aggregate their predictions through averaging. The method is known for its robustness in handling high-dimensional data and large datasets, making it versatile for various applications. The review covers recent theoretical and methodological advancements, focusing on the mathematical foundations driving the algorithm. Key topics include parameter selection, resampling mechanisms, and variable importance measures. The authors also discuss simplified models and their connections to nearest neighbor estimates and kernel methods, providing insights into the algorithm's performance and theoretical guarantees. The article aims to bridge the gap between theory and practice, offering a detailed guide for both experts and non-experts.The article provides a comprehensive review of the random forest algorithm, a popular method for classification and regression tasks. Proposed by L. Breiman in 2001, random forests combine multiple randomized decision trees and aggregate their predictions through averaging. The method is known for its robustness in handling high-dimensional data and large datasets, making it versatile for various applications. The review covers recent theoretical and methodological advancements, focusing on the mathematical foundations driving the algorithm. Key topics include parameter selection, resampling mechanisms, and variable importance measures. The authors also discuss simplified models and their connections to nearest neighbor estimates and kernel methods, providing insights into the algorithm's performance and theoretical guarantees. The article aims to bridge the gap between theory and practice, offering a detailed guide for both experts and non-experts.