  Beyond perturbation theory gauge-fixing becomes more involved due to the
Gribov-Singer ambiguity: The appearance of additional gauge copies requires to
define a procedure how to handle them. For the case of Landau gauge the
structure and properties of these additional gauge copies will be investigated.
Based on these properties gauge conditions are constructed to account for these
gauge copies.
  The dependence of the propagators on the choice of these complete
gauge-fixings will then be investigated using lattice gauge theory for
Yang-Mills theory. It is found that the implications for the infrared, and to
some extent mid-momentum behavior, can be substantial. In going beyond the
Yang-Mills case it turns out that the influence of matter can generally not be
neglected. This will be briefly discussed for various types of matter.
