This review provides an overview of machine learning interpretability methods, focusing on Explainable Artificial Intelligence (XAI). The paper discusses the challenges of using complex models, such as deep learning, which often act as "black boxes," making their decision-making processes difficult to understand. This lack of transparency has led to increased interest in XAI, which aims to develop methods that explain and interpret machine learning models. The review presents a taxonomy of interpretability methods, categorizing them based on their purpose and application. It covers various techniques for explaining black-box models, including post-hoc methods like Grad-CAM, LIME, SHAP, and others. The paper also discusses the importance of interpretability in sensitive domains such as healthcare and the need for fair, robust, and high-performing models. The review highlights the trade-off between model performance and interpretability, emphasizing the need for methods that balance both. It also addresses the limitations of current interpretability techniques and suggests future research directions. The paper concludes by emphasizing the importance of XAI in ensuring the trustworthiness and fairness of AI systems in real-world applications.This review provides an overview of machine learning interpretability methods, focusing on Explainable Artificial Intelligence (XAI). The paper discusses the challenges of using complex models, such as deep learning, which often act as "black boxes," making their decision-making processes difficult to understand. This lack of transparency has led to increased interest in XAI, which aims to develop methods that explain and interpret machine learning models. The review presents a taxonomy of interpretability methods, categorizing them based on their purpose and application. It covers various techniques for explaining black-box models, including post-hoc methods like Grad-CAM, LIME, SHAP, and others. The paper also discusses the importance of interpretability in sensitive domains such as healthcare and the need for fair, robust, and high-performing models. The review highlights the trade-off between model performance and interpretability, emphasizing the need for methods that balance both. It also addresses the limitations of current interpretability techniques and suggests future research directions. The paper concludes by emphasizing the importance of XAI in ensuring the trustworthiness and fairness of AI systems in real-world applications.