Graphene is the most two-dimensional platform currently available as a host for an electron gas, and offers promise to make observable a variety of effects in a perpendicular magnetic field. For example, recent advances in aligning graphene on a boron-nitride substrate have led to the creation of high-quality Moire patterns with large unit cells. Similar large-cell superlattices can also be created in twisted bilayers. In a perpendicular magnetic field, near zero energy the periodicity has little effect on the spectrum, but with increasing energy the spectrum evolves into the much-anticipated Hofstadter butterfly. The crossover between these behaviors is controlled by a saddle point in the zero-field spectrum. We demonstrate through a semiclassical analysis how the quantization of orbits changes as the saddle point is crossed, allowing the richness of the Hofstadter spectrum to emerge above it, and discuss some possible experimental consequences. We then consider graphene systems in much higher magnetic fields -- the quantum Hall regime -- where transport is controlled by edge states. For undoped graphene these edge states may have a helical nature. We discuss what happens when an "internal edge" is created in bilayer graphene using a split gate geometry, where a surprisingly rich internal structure emerges with a number of possible states. Such a geometry admits transport probes which potentially reveal different aspects of the internal structure, and we discuss our expectations for how the state of this internal edge can be reflected in such measurements.