A van der Waals heterostructure composed of a monolayer graphene flake on a hexagonal boron nitride (hBN) substrate exhibits a unique band structure due to the interplay between short- and long-wavelength effects. The spatially varying interlayer atomic registry leads to a local breaking of the carbon sublattice symmetry and a long-range moiré superlattice potential in the graphene. This results in a band structure with isolated superlattice minibands and a large band gap at charge neutrality, which can be tuned by varying the interlayer alignment. Magnetocapacitance measurements reveal previously unobserved fractional quantum Hall states, reflecting the massive Dirac dispersion from broken sublattice symmetry. At ultra-high magnetic fields, integer conductance plateaus appear at non-integer filling factors due to the emergence of the Hofstadter butterfly in a symmetry-broken Landau level. The ability to tailor the properties of electronic devices is a landmark achievement in modern technology. Artificial periodic superstructures can be used to modify the electronic band structure of existing materials. The band structure of pristine graphene consists of linearly dispersing energy bands that touch at two degenerate "Dirac points." This degeneracy is protected by the equivalence of the A and B triangular sublattices. Theory suggests that the electronic properties of graphene can be tuned via external periodic potentials. Long-wavelength superlattices have been predicted to lead to the formation of additional gapless Dirac points at finite energy, while atomic-scale modulations may turn graphene from a semimetal into a semiconductor. Recent advances in using hBN as a planar crystalline substrate have enabled the fabrication of multilayer heterostructures by sequential transfer of individual layers. The weak interlayer van der Waals forces in both graphene and hBN allow the fabrication of multilayer heterostructures. The beating of the mismatched lattices leads to the formation of a moiré pattern with a wavelength much larger than the lattice constant. The effect of the moiré on the graphene electronic structure can be decomposed into two parts: a λ-scale modulation of the graphene-hBN coupling and a subtle modulation of the local asymmetry between the graphene sublattices. The moiré pattern offers a unique opportunity to study the elementary problem of a charged quantum particle moving under the simultaneous influence of a periodic potential and a magnetic field in the normally inaccessible regime of more than one magnetic flux quantum per superlattice unit cell. In the absence of the superlattice, graphene is described by discrete, highly degenerate Landau levels. The periodic potential splits the flat LL bands into "Hofstadter minibands," separated by a hierarchy of self-similar minigaps. Despite the intricate structure of the Hofstadter spectrum, the densities corresponding to the fractal minigaps follow simple linear trajectories as a function of magnetic field. Magnetoresistance data show strongA van der Waals heterostructure composed of a monolayer graphene flake on a hexagonal boron nitride (hBN) substrate exhibits a unique band structure due to the interplay between short- and long-wavelength effects. The spatially varying interlayer atomic registry leads to a local breaking of the carbon sublattice symmetry and a long-range moiré superlattice potential in the graphene. This results in a band structure with isolated superlattice minibands and a large band gap at charge neutrality, which can be tuned by varying the interlayer alignment. Magnetocapacitance measurements reveal previously unobserved fractional quantum Hall states, reflecting the massive Dirac dispersion from broken sublattice symmetry. At ultra-high magnetic fields, integer conductance plateaus appear at non-integer filling factors due to the emergence of the Hofstadter butterfly in a symmetry-broken Landau level. The ability to tailor the properties of electronic devices is a landmark achievement in modern technology. Artificial periodic superstructures can be used to modify the electronic band structure of existing materials. The band structure of pristine graphene consists of linearly dispersing energy bands that touch at two degenerate "Dirac points." This degeneracy is protected by the equivalence of the A and B triangular sublattices. Theory suggests that the electronic properties of graphene can be tuned via external periodic potentials. Long-wavelength superlattices have been predicted to lead to the formation of additional gapless Dirac points at finite energy, while atomic-scale modulations may turn graphene from a semimetal into a semiconductor. Recent advances in using hBN as a planar crystalline substrate have enabled the fabrication of multilayer heterostructures by sequential transfer of individual layers. The weak interlayer van der Waals forces in both graphene and hBN allow the fabrication of multilayer heterostructures. The beating of the mismatched lattices leads to the formation of a moiré pattern with a wavelength much larger than the lattice constant. The effect of the moiré on the graphene electronic structure can be decomposed into two parts: a λ-scale modulation of the graphene-hBN coupling and a subtle modulation of the local asymmetry between the graphene sublattices. The moiré pattern offers a unique opportunity to study the elementary problem of a charged quantum particle moving under the simultaneous influence of a periodic potential and a magnetic field in the normally inaccessible regime of more than one magnetic flux quantum per superlattice unit cell. In the absence of the superlattice, graphene is described by discrete, highly degenerate Landau levels. The periodic potential splits the flat LL bands into "Hofstadter minibands," separated by a hierarchy of self-similar minigaps. Despite the intricate structure of the Hofstadter spectrum, the densities corresponding to the fractal minigaps follow simple linear trajectories as a function of magnetic field. Magnetoresistance data show strong