A number of exciting advances have been made in automated fact-checking thanks to increasingly larger datasets and more powerful systems, leading to improvements in the complexity of claims which can be accurately fact-checked. However, despite these advances, there are still desirable functionalities missing from the fact-checking pipeline. In this survey, we focus on the explanation functionality -- that is fact-checking systems providing reasons for their predictions. We summarize existing methods for explaining the predictions of fact-checking systems and we explore trends in this topic. Further, we consider what makes for good explanations in this specific domain through a comparative analysis of existing fact-checking explanations against some desirable properties. Finally, we propose further research directions for generating fact-checking explanations, and describe how these may lead to improvements in the research area.
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