Monolayer graphene in the quantum Hall has a set of quasi fourfold degenerate Landau levels at zero energy. They give rise to integer quantum Hall states with various symmetry-breaking patterns. Bernal-stacked bilayer graphene has an extra twofold degeneracy due to orbital degrees of freedom. This may lead to new phases with orbital coherence. I will present various attempts at mapping the phase diagram of these systems as a function of the electric bias between layers and applied field.