In principle the microscopic dynamics of interacting many-body quantum systems can be arbitrarily complicated and can depend on all possible details. However, on the macroscopic level novel universal phenomena can emerge, which may serve as a robust tool for classification of non-equilibrium processes in quantum simulations. I will present experimental studies with 87Rb spinor Bose-Einstein condensates in quasi-one-dimensional trapping potentials obtained in the Oberthaler group in Heidelberg. Employing quantum quenches, we bring the system out of equilibrium and observe transient universal phenomena associated with the emergence of a non-thermal fixed point. Introducing a method for extracting the quantum effective action from measurements, we are able to characterize the emergent phenomena and find a suppression of the four-vertex at low momenta in the highly occupied regime. Recent developments allow us to follow the system’s dynamics beyond the non-thermal fixed point and observe its approach to thermal equilibrium. We characterize the underlying quasi-particle excitations by probing the dispersion relations and find two Goldstone modes which are associated with the emergence of long-range coherence in the density and spin degree of freedom.