Higgs-confinement complementarity : Higgs and confining regions of a gauge theory are generally believed to be smoothly connected without a phase transition. Although such continuity was demonstrated to exist only for a certain class of gauge theories, the theorem has been applied more generally without much care. My work with collaborators in the context of quark-hadron transition suggests that Higgs and confining regimes of a gauge theory may well be separated by a phase transition under certain circumstances.