A final goal for thimble regularization of lattice field theories is the
application to lattice QCD and the study of its phase diagram. Gauge theories
pose a number of conceptual and algorithmic problems, some of which can be
addressed even in the framework of toy models. We report on our progresses in
this field, starting in particular from first successes in the study of one
link models.Comment: 7 pages, 2 figures. Talk given at the Lattice2015 Conferenc