Over an algebraically closed field, the substack of one dimensional formal groups is either a point (in characteristic zero) or an infinite chain of stacky points parametrizing heights. In characteristic zero, the closure of each point contains all points of greater height. This difference gives formal groups a rich geometric theory in positive and mixed characteristic, with connections to the Steenrod algebra, "p"-divisible groups, Dieudonné theory, and Galois representations. For example, the Serre-Tate theorem implies that the deformations of a group scheme are strongly controlled by those of its formal group, especially in the case of supersingular abelian varieties. For supersingular elliptic curves, this control is complete, and this is quite different from the characteristic zero situation where the formal group has no deformations.