A number of algorithms in the field of artificial intelligence offer poorly interpretable decisions. To disclose the reasoning behind such algorithms, their output can be explained by means of so-called evidence-based (or factual) explanations. Alternatively, contrastive and counterfactual explanations justify why the output of the algorithms is not any different and how it could be changed, respectively. It is of crucial importance to bridge the gap between theoretical approaches to contrastive and counterfactual explanation and the corresponding computational frameworks. In this work we conduct a systematic literature review which provides readers with a thorough and reproducible analysis of the interdisciplinary research field under study. We first examine theoretical foundations of contrastive and counterfactual accounts of explanation. Then, we report the state-of-the-art computational frameworks for contrastive and counterfactual explanation generation. In addition, we analyze how grounded such frameworks are on the insights from the inspected theoretical approaches. As a result, we highlight a variety of properties of the approaches under study and reveal a number of shortcomings thereof. Moreover, we define a taxonomy regarding both theoretical and practical approaches to contrastive and counterfactual explanation.

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