  In recent years the complex action problem of lattice field theory at finite
density was overcome for several system by mapping them to dual variables (flux
lines and surfaces). We illustrate this mapping for the case of the U(1) gauge
Higgs system and present some representative physics results for this model.
Conceptual challenges such as spectroscopy in the dual approach, as well as
algorithmic developments are discussed and related ideas for systems with
fermions are addressed. Models where the dual variables approach solves the
complex action problem can serve as reference systems for other approaches to
finite density lattice field theory and we discuss some examples. Finally we
address the strategy of a partial dualization in certain limits, e.g., for
strong coupling and large mass.
