In this talk I will discuss the elliptic genus of K3 (\phi_{K3}) both from a conformal field theory and an effective action point of view as an example of a BPS saturated quantity in string theory. In the former approach I will give evidence for an action of the Mathieu group M_{24} on the space of BPS states contributing to \phi_{K3} (Mathieu moonshine). On the effective action side I will present a new series of 1/4 BPS saturated one-loop amplitudes in type II string theory on K3xT^2 whose integrand can be related to derivatives of \phi_{K3}. I will evaluate explicitly a generating functional for this class of amplitudes and show that it is captured by the weight ten Igusa cusp form of Sp(4,Z). I conclude by speculating on possible algebraic implications of these results on the space of BPS states of the N=4 type II compactification.