  We present an extreme localization mechanism induced by a magnetic field for
tight-binding electrons in two-dimensional structures. This spectacular
phenomenon is investigated for a large class of tilings (periodic,
quasiperiodic, or random). We are led to introduce the Aharonov-Bohm cages
defined as the set of sites eventually visited by a wavepacket that can, for
particular values of the magnetic flux, be bounded. We finally discuss the
quantum dynamics which exhibits an original pulsating behaviour.
