The infrared fixed point of graphene under the renormalization group flow is a relatively under studied yet important example of a boundary conformal field theory with a number of remarkable properties. It has a close relationship with three dimensional QED. It maps to itself under electric-magnetic duality. Moreover, it along with its supersymmetric cousins all possess an exactly marginal coupling -- the charge of the electron. I will review past work on this model and also discuss my own contributions which have focused on understanding the boundary contributions to the anomalous trace of the stress tensor and their role in helping to understand the structure of boundary conformal field theory. If there is time, I hope to present some exciting new results on the hemisphere partition function for supergraphene, its duality properties, and an exact computation of the conductivity at arbitrary values of the interaction strength.
