I will discuss our efforts to describe the evolution of many-body quantum systems from the moment they are taken far from equilibrium to the moment they reach a new equilibrium. We unveil different behaviors at different time scales and show how information about the spectrum of a many-body quantum system can be extracted by the sole analysis of its time evolution. This allows us to determine whether the system is integrable or chaotic and if it is or not close to a metal-insulator transition. In addition, using full random matrices, we obtain analytical expressions for the survival probability, density imbalance, and out-of-time-ordered correlator. They serve as references for the analysis of realistic systems and motivate an expression that describes very well the entire evolution of the survival probability for a chaotic spin-1/2 model.