Niels Bohr’s complementarity principle is a tenuous synthesis of seemingly discrepant theoretical approaches based on a comprehensive analysis of relevant experimental results. Yet the role of complementarity, and the experimentalist-minded approach behind it, were not confined to a provisional best-available synthesis of well-established experimental results alone. They were also pivotal in discovering and explaining the phenomenon of quantum tunneling in its various forms. The core principles of Bohr’s method and the ensuing complementarity account of quantum phenomena remain highly relevant guidelines (...) in the current controversial debate and in experimental work on quantum tunneling times. (shrink)