Artificial Intelligence (AI) is increasingly transforming atmospheric and space sciences by enabling the analysis of complex datasets and improving predictions in climate modelling, weather forecasting, satellite monitoring, spacecraft anomaly detection, and astrophysical research. However, deep learning models often function as “black boxes,” limiting transparency and reducing confidence in their predictions. This survey, based on peer-reviewed journal articles, conference papers, and authoritative reviews published between 2020 and 2026, examines the role of Explainable Artificial Intelligence (XAI) in addressing these challenges. Techniques including feature importance, sensitivity analysis, visualization, counterfactual and prototype-based explanations, rule-based models, and transparent documentation can improve interpretability, reliability, causality, fairness, privacy, and trust. By connecting data-driven AI with established physical principles, XAI strengthens scientific credibility, supports safer operational decisions, and promotes responsible AI adoption. The study argues that XAI is essential for advancing scientific discovery and societal resilience in atmospheric and space applications.