Explainable Artificial Intelligence (XAI) seeks to make AI systems more transparent and understandable to users. This review examines the various techniques developed to achieve explainability in AI models and their applications across different domains. We discuss methods such as feature attribution, model simplification, and example-based explanations, highlighting their strengths and limitations. Additionally, we explore the importance of XAI in critical fields like healthcare, finance, and law. The findings underscore the necessity of explainability for trust, accountability, and ethical AI deployment, pointing towards future directions in the field.