The technological development of graphene has generated new high-quality systems offer access to the earlier inaccessible extremes of quantum physics. When graphene is placed on an atomically flat substrate with hexagonal lattice with a close lattice constant, such as boron nitride (hBN), and their crystalline axes are aligned, a long-wavelength perfectly periodic moiré pattern forms for electrons in graphene. In this talk, various regimes of possible moiré minibands at zero magnetic field [Phys. Rev. B 87, 245408 (2013); Phys. Rev. B 88, 205418; Phys. Rev. B 88, 155415 (2013)] and strong magnetic field [Nature 497, 594 (2013), arXiv:1310.8578] will be discussed. Experimentally available magnetic fields are enough to provide flux Phi through the moiré superlattice cell comparable to the magnetic flux quantum Phi_0 and reach the regime of fractal Hofstadter spectra. As a result, a single device can offer a multiplicity of two-dimensional electron systems, realised at rational flux values  Phi= Phi_0, = Phi_0/2, 2= Phi_0/3, etc., each with its own intricate topological properties, including quantum Hall effect physics related to the effective Landau levels emerging from these magnetic minibands at the nearby range of magnetic fields.