The increasing deployment of complex, learning-based artificial intelligence systems has heightened concerns regarding transparency, accountability, and trust, as improvements in predictive performance often come at the expense of interpretability. This chapter provides a structured, non-technical introduction to explainable artificial intelligence (XAI), clarifying core concepts, systematizing explanation methods, and highlighting their practical limitations. It presents a consolidated XAI framework that differentiates between intrinsic and post-hoc approaches, local and global explanations, model-agnostic and model-specific methods, and prominent explanation families across various data types. Using targeted case studies in credit scoring and medical imaging, the chapter illustrates how context, stakeholder requirements, and normative constraints influence the selection of explanation methods. The analysis also addresses key challenges, including explanation fidelity, robustness, feature dependence, human-centered design, and lifecycle governance.