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.v