  The emergence of macroscopic coherence in a many-body quantum system is a
ubiquitous phenomenon across different physical systems and scales. This
Chapter reviews key concepts characterizing such systems (correlation
functions, condensation, quasi-condensation) and applies them to the study of
emerging non-equilibrium features in the dynamical path towards such a
highly-coherent state: particular emphasis is placed on emerging universal
features in the dynamics of conservative and open quantum systems, their
equilibrium or non-equilibrium nature, and the extent that these can be
observed in current experiments with quantum gases. Characteristic examples
include symmetry-breaking in the Kibble-Zurek mechanism, coarsening and
phase-ordering kinetics, and universal spatiotemporal scalings around
non-thermal fixed points and in the context of the Kardar- Parisi-Zhang
equation; the Chapter concludes with a brief review of the potential relevance
of some of these concepts in modelling the large-scale distribution of dark
matter in the universe.
