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RationalDeep learning (DL) has demonstrated a remarkable performance in diagnostic imaging for various diseases and modalities and therefore has a high potential to be used as a clinical tool. However, current practice shows low deployment of these algorithms in clinical practice, because DL algorithms lack transparency and trust due to their underlying black-box mechanism. For successful employment, explainable artificial intelligence (XAI) could be introduced to close the gap between the medical professionals and the DL algorithms. In this literature review, XAI methods available for magnetic resonance (MR), computed tomography (CT), and positron emission tomography (PET) imaging are discussed and future suggestions are made.MethodsPubMed, Embase.com and Clarivate Analytics/Web of Science Core Collection were screened. Articles were considered eligible for inclusion if XAI was used (and well described) to describe the behavior of a DL model used in MR, CT and PET imaging.ResultsA total of 75 articles were included of which 54 and 17 articles described post and ad hoc XAI methods, respectively, and 4 articles described both XAI methods. Major variations in performance is seen between the methods. Overall, post hoc XAI lacks the ability to provide class-discriminative and target-specific explanation. Ad hoc XAI seems to tackle this because of its intrinsic ability to explain. However, quality control of the XAI methods is rarely applied and therefore systematic comparison between the methods is difficult.ConclusionThere is currently no clear consensus on how XAI should be deployed in order to close the gap between medical professionals and DL algorithms for clinical implementation. We advocate for systematic technical and clinical quality assessment of XAI methods. Also, to ensure end-to-end unbiased and safe integration of XAI in clinical workflow, (anatomical) data minimization and quality control methods should be included.