  Closed quantum systems far from thermal equilibrium can show universal
dynamics near attractor solutions, known as non-thermal fixed points,
generically in the form of scaling behavior in space and time. A systematic
classification and comprehensive understanding of such scaling solutions are
tasks of future developments in non-equilibrium quantum many-body theory. In
this tutorial review, we outline several analytical approaches to non-thermal
fixed points and summarize corresponding numerical and experimental results.
The analytic methods include a non-perturbative kinetic theory derived within
the two-particle irreducible effective-action formalism, as well as a
low-energy effective field theory framework. As one of the driving forces of
this research field are numerical simulations, we summarize the main results of
exemplary cases of universal dynamics in ultracold Bose gases. This encompasses
quantum vortex ensembles in turbulent superfluids as well as recently observed
real-time instanton solutions in one-dimensional spinor condensates.
