  Flat surfaces that correspond to meromorphic $1$-forms or to meromorphic
quadratic differentials containing poles of order two and higher are surfaces
of infinite area. We classify groups that appear as Veech groups of translation
surfaces with poles. We characterize those surfaces such that their
$GL^{+}(2,\mathbb{R})$-orbit or their $SL(2,\mathbb{R})$-orbit is closed.
Finally, we provide a way to determine the Veech group for a typical infinite
surface in a given chamber of a stratum.
