This open access five-volume set constitutes the refereed proceedings of the Second World Conference on Explainable Artificial Intelligence, xAI 2025, held in Istanbul, Turkey, during July 2025. The 96 revised full papers presented in these proceedings were carefully reviewed and selected from 224 submissions. The papers are organized in the following topical sections: Volume I: Concept-based Explainable AI; human-centered explainability; explainability, privacy, and fairness in trustworthy AI; and XAI in healthcare. Volume II: Rule-based XAI systems & actionable explainable AI; features importance-based XAI; novel post-hoc & ante-hoc XAI approaches; and XAI for scientific discovery. Volume III: Generative AI meets explainable AI; Intrinsically interpretable explainable AI; benchmarking and XAI evaluation measures; and XAI for representational alignment. Volume IV: XAI in computer vision; counterfactuals in XAI; explainable sequential decision making; and explainable AI in finance & legal frameworks for XAI technologies. Volume V: Applications of XAI; human-centered XAI & argumentation; explainable and interactive hybrid decision making; and uncertainty in explainable AI.