Recently, eXplainable AI (XAI) research has focused on counterfactual explanations as post-hoc justifications for AI-system decisions (e.g., a customer refused a loan might be told “if you asked for a loan with a shorter term, it would have been approved”). Counterfactuals explain what changes to the input-features of an AI system change the output-decision. However, there is a sub-type of counterfactual, semi-factuals, that have received less attention in AI (though the Cognitive Sciences have studied them more). This paper surveys semi-factual explanation, summarising historical and recent work. It defines key desiderata for semi-factual XAI, reporting benchmark tests of historical algorithms (as well as a novel, naïve method) to provide a solid basis for future developments.