Abstract: In this talk I will present two stories of emergent uiversality in thermally isolated driven systems. In the first I will show how unitary dynamics constraints energy distribution in a repeatedly driven thermally isolated system (microwave setup). I will present generalized fluctuation relations and will show that they imply a dynamical phase transition between canonical like and wide regimes. In the second part of the talk, if time permits, I will discuss universal scaling of energy, entropy and defect generation for quench dynamics through quantum critical points. In particular, I will show how quantum Kibble-Zurek and other related scalings follow from the adiabatic perturbation theory.