The van der Waals forces in 2D heterostructures are weak enough that lattices are not constrained to be commensurate--yet strong enough that the layers interact, structurally and electronically. We are looking at two regimes in twisted bilayer graphene in which incommensurate structures have interesting transport properties. At small angles, structural relaxation leads to the formation of AB and BA domains. We observe potential signatures of topologically protected conduction along the resulting domain walls. We also are interested in twisted bilayer graphene with 30 degree angle, which is a quasicrystal. Quasicrystals can have modified transport properties like localization and unusual scaling.