Interpretable Machine Learning (IML) is a rapidly growing research area focused on developing models and techniques that make machine learning decisions understandable, transparent, and trustworthy to humans. Foundational studies distinguish between inherently interpretable models, such as decision trees, rule-based systems, and linear models, and post-hoc explanation methods that interpret complex models like deep neural networks using techniques such as LIME, SHAP, saliency maps, and feature attribution. Recent research emphasizes model-agnostic approaches, counterfactual explanations, causal inference-based interpretations, and attention mechanisms to provide both global and local interpretability. Applications span high-stakes domains including healthcare, finance, autonomous systems, and legal decision-making, where understanding model reasoning is critical for trust, accountability, and compliance. Current trends also explore combining interpretability with fairness, robustness, and uncertainty quantification, establishing IML as a crucial component in developing responsible and transparent AI systems.