How an interacting many-particle system which is initially out of equilibrium evolves in time, is a challenging question, especially for large system sizes where numerical simulations are difficult. The most puzzling issue is understanding the onset of thermalization, a process in which the system completely looses memory of its initial state, with the long time behavior characterized by only one or two parameters. Understanding this issue is important as ideal, thermally isolated systems, and their time-evolution can now be routinely studied in experiments. Using a novel time-dependent renormalization group approach I will show how a reduced part of a strongly interacting system can look effectively classical (or thermal) by being characterized by a dissipation and a noise, even though the system as a whole is closed and in a pure quantum state. I will also show that a closed quantum system during its time-evolution from a nonequilibrium initial state can show a new kind of dynamical phase transition where observables can behave in a non-analytic manner in time.