  We theoretically investigate the electronic structures of moir\'{e}
superlattices arising in monolayer / bilayer graphene stacked on hexagonal
boron nitride (hBN) in presence and absence of magnetic field. We develop an
effective continuum model from a microscopic tight-binding lattice Hamiltonian,
and calculate the electronic structures of graphene-hBN systems with different
rotation angles. Using the effective model, we explain the characteristic band
properties such as the gap opening at the corners of the superlattice Brillouin
zone (mini-Dirac point). We also investigate the energy spectrum and quantum
Hall effect of graphene-hBN systems in uniform magnetic field and demonstrate
the evolution of the fractal spectrum as a function of the magnetic field. The
spectrum generally splits in the valley degrees of freedom ($K$ and $K'$) due
to the lack of the inversion symmetry, and the valley splitting is more
significant in bilayer graphene on hBN than in monolayer graphene on hBN
because of the stronger inversion-symmetry breaking in bilayer.
