  We performed calculations of electronic, optical and transport properties of
graphene on hBN with realistic moir\'e patterns. The latter are produced by
structural relaxation using a fully atomistic model. This relaxation turns out
to be crucially important for electronic properties. We describe experimentally
observed features such as additional Dirac points and the "Hofstadter
butterfly" structure of energy levels in a magnetic field. We find that the
electronic structure is sensitive to many-body renormalization of the local
energy gap.
