Explainable Artificial Intelligence (XAI) aims to make AI systems more transparent and interpretable, allowing users to understand and trust their decisions. This paper discusses the importance of explainability in AI, especially in critical applications like healthcare and autonomous systems, where understanding the decision-making process is essential. It presents two methods for explaining AI predictions: sensitivity analysis (SA) and layer-wise relevance propagation (LRP). SA measures the sensitivity of predictions to input changes, while LRP decomposes predictions into input variables, providing a more accurate interpretation. The paper evaluates these methods on image, text, and video classification tasks, showing that LRP produces more reliable and interpretable explanations than SA. The results highlight the need for explainable AI in ensuring trust, compliance, and effective use of AI systems in various domains. The paper also discusses future research directions, including the theoretical foundations of explainability and its application to new domains.Explainable Artificial Intelligence (XAI) aims to make AI systems more transparent and interpretable, allowing users to understand and trust their decisions. This paper discusses the importance of explainability in AI, especially in critical applications like healthcare and autonomous systems, where understanding the decision-making process is essential. It presents two methods for explaining AI predictions: sensitivity analysis (SA) and layer-wise relevance propagation (LRP). SA measures the sensitivity of predictions to input changes, while LRP decomposes predictions into input variables, providing a more accurate interpretation. The paper evaluates these methods on image, text, and video classification tasks, showing that LRP produces more reliable and interpretable explanations than SA. The results highlight the need for explainable AI in ensuring trust, compliance, and effective use of AI systems in various domains. The paper also discusses future research directions, including the theoretical foundations of explainability and its application to new domains.