  Twisted graphene bilayers show a complex electronic structure, further
modified by interaction effects. The main features can be obtained from
effective models, which make use a few phenomenological parameters. We analyze
the influence of effects at the atomic scale, such as interlayer hopping and
lattice relaxation, on the electronic bands. We assume that the twist angle and
the size of the Moir\'e pattern is fixed, as it is usually the case in
experiments. We obtain a strong dependence of the electronic structure on
details of the models at the atomic scale. We discuss how to incorporate this
dependence on effective models
