  Systems with long-range interactions (LRI) display unusual thermodynamical
and dynamical properties that stem from the non-additive character of the
interaction potential. We focus in this work on the lack of relaxation to
thermal equilibrium when a LRI system is started out-of-equilibrium. Several
attempts have been made at predicting the so-called quasi-stationary state
(QSS) reached by the dynamics and at characterizing the resulting transition
between magnetized and non-magnetized states. We review in this work recent
theories and interpretations about the QSS. Several theories exist but none of
them has provided yet a full account of the dynamics found in numerical
simulations.
