Gravitational Instantons are first introduced by Hawking as the building block for this Euclidean quantum gravity theory. Mathematically, they are non-compact hyperK\"ahler 4-manifolds with L^2
curvature tensor. These are always the bubbling limits of K3 surfaces and thus serve as the step stones to understand the K3 metrics. From the volume growth and the curvature decay, Sun-Zhang showed that there are exactly 6 types of them and labled by ALE, ALF, ALG, ALH, ALG*, ALH*. In this talk, I will survey the recent development of gravitational instanton and then discuss the classifications and the Torelli theorem for the ALH*-gravitational instantons. This is based on joint works with T. Collins, A. Jacob and T.-J. Lee.