Systems out of equilibrium, as they relax, can thermalize to equilibrium states. Here we focus on what happens during this dynamics. We show, for instance, that two-time correlations can present a hierarchy of algebraic relaxation decays which can be predicted with simple steps. Furthermore, we will show in which conditions you can tap on finite systems to probe non-equilibrium steady state physics, and we will conclude by discussing how entanglement phase transitions, inspired by measurement-induced phase transition can be observed in completely unitary setups.