  We present a study of different models of local disorder in graphene. Our
focus is on the main effects that vacancies -- random, compensated and
uncompensated --, local impurities and substitutional impurities bring into the
electronic structure of graphene. By exploring these types of disorder and
their connections, we show that they introduce dramatic changes in the low
energy spectrum of graphene, viz. localized zero modes, strong resonances, gap
and pseudogap behavior, and non-dispersive midgap zero modes.
