The growing reliance on opaque deep learning models in critical domains has intensified the demand for transparency, accountability, and interpretability of artificial intelligence systems. Explainable Artificial Intelligence (XAI) seeks to address this through methods that clarify how models make predictions, fostering informed oversight and trust. This review synthesizes foundational concepts in XAI, distinguishing interpretability from explainability and contrasting intrinsic with post-hoc methods, as well as local with global explanations. It surveys major techniques such as feature attribution, gradient-based methods, surrogate models, counterfactual reasoning, and inherently interpretable architectures alongside widely used tools, frameworks, and evaluation metrics, including fidelity, human interpretability, robustness, and efficiency. Applications in healthcare, finance, law, and autonomous systems are discussed, highlighting domain-specific interpretability needs. Persistent challenges, including inconsistent terminology, subjective evaluation, and adversarial vulnerabilities, are examined. The review concludes with emerging directions in human-centered, real-time, and multimodal explanations, aiming to guide the design of XAI systems that are both technically sound and aligned with societal expectations.