‘Mathieu Moonshine’, namely the observation that the elliptic genus of K3 shows signs of an underlying Mathieu M24 group symmetry, will be introduced, exhibiting the parallels to the more familiar Monstrous Moonshine phenomenon. I will review how Mathieu Moonshine has now been proven, but that a conceptual and geometric interpretation of the phenomenon is still missing. I will then explain recent attempts at uncovering the mircoscopic origin for Mathieu Moonshine.