During its dynamical evolution far from equilibrium a many-body system can reach a non-thermal fixed point. The general concept of such non-thermal fixed points is discussed for various configurations of ultracold Bose gases. It is demonstrated that the fixed points, at which the system exhibits universal properties, can be be closely related to (quasi)topological excitations and superfluid turbulence. Our results provide a long-sought link between weak wave turbulence and (strong) quantum turbulence phenomena. The dynamics following an initial quench will be shown to be affected by a non-thermal fixed point in a generic way. This has observable consequences for Kibble-Zurek-type protocols, the formation of a Bose-Einstein condensate in a three-dimensional gas, or soliton gases forming in one spatial dimension. For spinor gases the non-thermal fixed points are demonstrated to correspond to more general pattern formation processes.

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