In 2010, Eguchi--Ooguri--Tachikawa observed an unexpected relation between K3 elliptic genus and the sporadic group M24. In this talk I'll briefly review the recent developments on the topic of moonshine. In particular I will describe a more general relation between mock modular forms and finite groups, using Niemeier lattices as the starting point and including the M24 observation as a special case. I will also discuss various approaches in attempting to understand these mysterious relations, focusing on the study of compactification of heterotic strings on K3 surfaces. This talk will be based on joint work with Duncan--Harvey and with Dong--Harrison--Kachru--Whalen--Wrase.