However, the quantum Zeno effect (QZE) does not necessarily freeze everything. On the contrary, for frequent projections onto a multi-dimensional subspace, the system can evolve away from its initial state, although it remains in the subspace defined by the measurement. This continuing time evolution within the projected subspace is named "quantum Zeno dynamics" and has interesting features. In particular, it is reversible for a wide class of systems.

We give an *elementary introduction* to these issues and then recast the quantum Zeno effect in terms of an adiabatic theorem, and view it as a consequence of the dynamical coupling to another quantum system: in the strong coupling limit the system is forced to evolve in a set of orthogonal subspaces of the total Hilbert space and a dynamical superselection rule arises . Some significant examples will be proposed and their practical relevance discussed.

We focus on decoherence, irreversibility and decoherence-free subspaces.