  Explainable Artificial Intelligence (XAI) has become increasingly significant
for improving the interpretability and trustworthiness of machine learning
models. While saliency maps have stolen the show for the last few years in the
XAI field, their ability to reflect models' internal processes has been
questioned. Although less in the spotlight, example-based XAI methods have
continued to improve. It encompasses methods that use examples as explanations
for a machine learning model's predictions. This aligns with the psychological
mechanisms of human reasoning and makes example-based explanations natural and
intuitive for users to understand. Indeed, humans learn and reason by forming
mental representations of concepts based on examples.
  This paper provides an overview of the state-of-the-art in natural
example-based XAI, describing the pros and cons of each approach. A "natural"
example simply means that it is directly drawn from the training data without
involving any generative process. The exclusion of methods that require
generating examples is justified by the need for plausibility which is in some
regards required to gain a user's trust. Consequently, this paper will explore
the following family of methods: similar examples, counterfactual and
semi-factual, influential instances, prototypes, and concepts. In particular,
it will compare their semantic definition, their cognitive impact, and added
values. We hope it will encourage and facilitate future work on natural
example-based XAI.
