Complex cobordism is among the most important generalized cohomology theories that one encounters in homotopy theory. This is because of the deep connection between complex cobordism, complex orientations, and formal group laws. In this talk, we will investigate the G-equivariant analogue of this story, where G is some group. In particular, we will calculate the complex cobordism ring of Z/2-manifolds, and explain how this calculation leads to a new theory of "filtered" Z/2-equivariant formal group laws.