The random forest algorithm, introduced by L. Breiman in 2001, is a powerful method for classification and regression. It combines multiple randomized decision trees and aggregates their predictions through averaging. It excels in high-dimensional settings and is versatile, adaptable to various tasks, and provides variable importance measures. This review explores recent theoretical and methodological advances in random forests, focusing on the mathematical principles driving the algorithm, parameter selection, resampling, and variable importance. The article aims to provide non-experts with a clear understanding of the key ideas. Random forests are built by growing multiple trees on bootstrap samples of the data and using random subsets of features for splitting. Each tree's predictions are averaged to produce the final result. The algorithm is effective for both regression and classification tasks, with the latter using majority voting. The method is computationally intensive but can be parallelized, making it suitable for large datasets. Theoretical studies have shown that random forests can be consistent under certain conditions, such as when the number of trees grows with the sample size. The performance of random forests depends on parameters like the number of trees, the number of features considered at each split, and the minimum number of samples per leaf. These parameters influence the model's accuracy and computational efficiency. Theoretical analysis of random forests has revealed connections to nearest neighbor methods and kernel methods. The resampling mechanism, which involves bootstrap sampling, plays a crucial role in the algorithm's performance. However, the theoretical understanding of random forests remains limited, with much of the analysis focusing on simplified models. Recent studies have explored the consistency of random forests in various contexts, including regression and classification. The use of random forests in practical applications, such as data science hackathons, chemoinformatics, ecology, and bioinformatics, highlights their versatility and effectiveness. Theoretical advancements have also contributed to a better understanding of the algorithm's behavior, including its ability to handle high-dimensional data and its robustness to overfitting. In summary, random forests are a powerful and versatile method for data analysis, with strong theoretical foundations and practical applications. The algorithm's ability to handle high-dimensional data, provide variable importance measures, and adapt to various tasks makes it a valuable tool in modern data science. Ongoing research continues to enhance the theoretical understanding and practical implementation of random forests.The random forest algorithm, introduced by L. Breiman in 2001, is a powerful method for classification and regression. It combines multiple randomized decision trees and aggregates their predictions through averaging. It excels in high-dimensional settings and is versatile, adaptable to various tasks, and provides variable importance measures. This review explores recent theoretical and methodological advances in random forests, focusing on the mathematical principles driving the algorithm, parameter selection, resampling, and variable importance. The article aims to provide non-experts with a clear understanding of the key ideas. Random forests are built by growing multiple trees on bootstrap samples of the data and using random subsets of features for splitting. Each tree's predictions are averaged to produce the final result. The algorithm is effective for both regression and classification tasks, with the latter using majority voting. The method is computationally intensive but can be parallelized, making it suitable for large datasets. Theoretical studies have shown that random forests can be consistent under certain conditions, such as when the number of trees grows with the sample size. The performance of random forests depends on parameters like the number of trees, the number of features considered at each split, and the minimum number of samples per leaf. These parameters influence the model's accuracy and computational efficiency. Theoretical analysis of random forests has revealed connections to nearest neighbor methods and kernel methods. The resampling mechanism, which involves bootstrap sampling, plays a crucial role in the algorithm's performance. However, the theoretical understanding of random forests remains limited, with much of the analysis focusing on simplified models. Recent studies have explored the consistency of random forests in various contexts, including regression and classification. The use of random forests in practical applications, such as data science hackathons, chemoinformatics, ecology, and bioinformatics, highlights their versatility and effectiveness. Theoretical advancements have also contributed to a better understanding of the algorithm's behavior, including its ability to handle high-dimensional data and its robustness to overfitting. In summary, random forests are a powerful and versatile method for data analysis, with strong theoretical foundations and practical applications. The algorithm's ability to handle high-dimensional data, provide variable importance measures, and adapt to various tasks makes it a valuable tool in modern data science. Ongoing research continues to enhance the theoretical understanding and practical implementation of random forests.