Mathieu Moonshine and symmetries of K3 s-models

A recent observation by Eguchi, Ooguri and Tachikawa (EOT) suggests a relationship between the largest Mathieu group ??24 and the elliptic genus of K3. This correspondence would be naturally explained by the existence of a non-linear s-model on K3 with the Mathieu group as its group of symmetries. However, all possible symmetry groups of K3 models have been recently classified and none of them contains ??24. We review the evidence in favour of the EOT conjecture and discuss the open problems in its physical interpretation.