  During the last 40 years, Monte Carlo calculations based upon Importance
Sampling have matured into the most widely employed method for determinig first
principle results in QCD. Nevertheless, Importance Sampling leads to
spectacular failures in situations in which certain rare configurations play a
non-secondary role as it is the case for Yang-Mills theories near a first order
phase transition or quantum field theories at finite matter density when
studied with the re-weighting method. The density-of-states method in its LLR
formulation has the potential to solve such overlap or sign problems by means
of an exponential error suppression. We here introduce the LLR approach and its
generalisation to complex action systems. Applications include U(1), SU(2) and
SU(3) gauge theories as well as the Z3 spin model at finite densities and
heavy-dense QCD.
