I will present results for the quench dynamics of one-dimensional interacting bosons under two circumstances. One is when the bosons are in the vicinity of the superfluid-Mott quantum critical point, while the second is when the bosons are in a disordered potential which can drive the system into a Bose glass phase. I will show that the dynamics following a quench can be quite complex by being characterized by three regimes. One is a short time perturbatively accessible regime which depends on microscopic parameters, the second is an intermediate time prethermalized regime where inelastic effects are weak and correlation functions can show universal scaling behavior which is quantified by a nonequilibrium generalization of the Callan-Symanzik equations. The third is a long time regime where inelastic effects become important. For the dynamics in the inelastic regime I will construct a novel quantum kinetic equation that accounts for multi-particle scattering between bosons, and discuss how the combined effect of interactions and (weak) disorder can thermalize the system.