  Following a fast initial breakthrough in graph based learning, Graph Neural
Networks (GNNs) have reached a widespread application in many science and
engineering fields, prompting the need for methods to understand their decision
process.
  GNN explainers have started to emerge in recent years, with a multitude of
methods both novel or adapted from other domains. To sort out this plethora of
alternative approaches, several studies have benchmarked the performance of
different explainers in terms of various explainability metrics. However, these
earlier works make no attempts at providing insights into why different GNN
architectures are more or less explainable, or which explainer should be
preferred in a given setting.
  In this survey, we fill these gaps by devising a systematic experimental
study, which tests ten explainers on eight representative architectures trained
on six carefully designed graph and node classification datasets. With our
results we provide key insights on the choice and applicability of GNN
explainers, we isolate key components that make them usable and successful and
provide recommendations on how to avoid common interpretation pitfalls. We
conclude by highlighting open questions and directions of possible future
research.
