This review discusses the growing importance of machine learning interpretability in today's society, where ML systems are increasingly used in various domains and decision-making processes. The paper highlights the need for interpretability due to the complexity of ML models, which often act as "black boxes" and obscure their decision-making processes. The research community has recognized this issue and has focused on developing both interpretable models and explanation methods. However, there is no consensus on how to assess the quality of these explanations, leading to the need for a comprehensive review of current research in this field. The paper emphasizes the societal impact of ML interpretability, particularly in high-stakes decision-making areas such as healthcare, criminal justice, and finance. It also discusses the challenges in achieving interpretability, including the need for transparency, accountability, and fairness in ML systems. The paper reviews the historical context of interpretability, noting that interest in explaining AI systems has grown significantly in recent years, driven by the increasing use of ML in critical applications. The paper also explores the terminology and concepts related to interpretability, noting that while the terms "interpretability" and "explainability" are often used interchangeably, they have distinct meanings in the context of ML. The paper discusses the importance of interpretability in ensuring that ML systems are trustworthy, transparent, and fair. It also highlights the role of interdisciplinary research in advancing the field of ML interpretability, emphasizing the need for collaboration between data science, human science, and human-computer interaction. The paper reviews the current state of research in ML interpretability, discussing various methods and metrics used to assess the quality of explanations. It also highlights the challenges in evaluating these methods and the need for standardized metrics. The paper concludes that interpretability is essential for the development of trustworthy and transparent ML systems, and that further research is needed to address the challenges in this field.This review discusses the growing importance of machine learning interpretability in today's society, where ML systems are increasingly used in various domains and decision-making processes. The paper highlights the need for interpretability due to the complexity of ML models, which often act as "black boxes" and obscure their decision-making processes. The research community has recognized this issue and has focused on developing both interpretable models and explanation methods. However, there is no consensus on how to assess the quality of these explanations, leading to the need for a comprehensive review of current research in this field. The paper emphasizes the societal impact of ML interpretability, particularly in high-stakes decision-making areas such as healthcare, criminal justice, and finance. It also discusses the challenges in achieving interpretability, including the need for transparency, accountability, and fairness in ML systems. The paper reviews the historical context of interpretability, noting that interest in explaining AI systems has grown significantly in recent years, driven by the increasing use of ML in critical applications. The paper also explores the terminology and concepts related to interpretability, noting that while the terms "interpretability" and "explainability" are often used interchangeably, they have distinct meanings in the context of ML. The paper discusses the importance of interpretability in ensuring that ML systems are trustworthy, transparent, and fair. It also highlights the role of interdisciplinary research in advancing the field of ML interpretability, emphasizing the need for collaboration between data science, human science, and human-computer interaction. The paper reviews the current state of research in ML interpretability, discussing various methods and metrics used to assess the quality of explanations. It also highlights the challenges in evaluating these methods and the need for standardized metrics. The paper concludes that interpretability is essential for the development of trustworthy and transparent ML systems, and that further research is needed to address the challenges in this field.