The article provides a comprehensive overview of European regulations, the GDPR and the AI Act, focusing on the right to explanation for individual decisions inferred from high-risk AI systems and automated decision-making. It analyses the concept of the right to explanation in automated decision-making processes, emphasizing the legal obligations surrounding the provision of meaningful information pre- and post-decision. The paper examines explainable AI (XAI) methods in this context, categorizing them as intrinsic and post-hoc, with examples like decision trees, Shapley values and Local Interpretable Model-Agnostic Explanations (LIME). By analysing the legal and technical dimensions together, insights into the complex interplay between data protection, AI regulation, and the quest for transparency in the EU acquis are made.