BACKGROUND: Artificial intelligence is playing an increasingly important role in radiology. However, more and more often it is no longer possible to reconstruct decisions, especially in the case of new and powerful methods from the field of deep learning. The resulting models fulfill their function without the users being able to understand the internal processes and are used as so-called black boxes. Especially in sensitive areas such as medicine, the explainability of decisions is of paramount importance in order to verify their correctness and to be able to evaluate alternatives. For this reason, there is active research going on to elucidate these black boxes. METHOD: This review paper presents different approaches for explainable artificial intelligence with their advantages and disadvantages. Examples are used to illustrate the introduced methods. This study is intended to enable the reader to better assess the limitations of the corresponding explanations when meeting them in practice and strengthen the integration of such solutions in new research projects. RESULTS AND CONCLUSION: Besides methods to analyze black-box models for explainability, interpretable models offer an interesting alternative. Here, explainability is part of the process and the learned model knowledge can be verified with expert knowledge. KEY POINTS: · The use of artificial intelligence in radiology offers many possibilities to provide safer and more efficient medical care. This includes, but is not limited to support during image acquisition and processing or for diagnosis.. · Complex models can achieve high accuracy, but make it difficult to understand data processing.. · If the explainability is already taken into account during the planning of the model, methods can be developed that are powerful and interpretable at the same time.. CITATION FORMAT: · Gallée L, Kniesel H, Ropinski T et al. Artificial intelligence in radiology - beyond the black box. Fortschr Röntgenstr 2023; 195: 797 - 803.