The article begins with an overview of international regulations governing the matter of algorithmic transparency and the explainability of AI systems, with an emphasis on European Union regulations. The focus of the paper is on the functional and structural analysis of the concept of transparency. This analysis demonstrates the legitimacy of the legal demand for algorithmic transparency, but also points to inherent obstacles to its realization. Therefore, the lay understanding of transparency—as openness of the of the software itself, as well as the data entering and exiting an AI system—is not achievable in reality. What is currently feasible includes: informing the public about the risks and shortcomings of AI; developing technical and non-technical transparency standards; self-assessment of risks and risk mitigation measures by AI system operators; storing data on certain aspects of AI system functioning for later analysis and proof of deficiencies; and enabling legal protection for individuals and legal entities against rights violations caused by the application of AI. In short, these are indirect measures whose actual effects cannot yet be reliably assessed, as the system has only recently been established.