Relaxation of periodically driven systems is accompanied by quantum noise. It leads to a finite width of the distribution over the states of the system even for T=0, the effect of quantum heating. It also leads to switching between metastable states via the mechanism of quantum activation that has no analog in equilibrium systems. These phenomena will be discussed using, as a model, a driven nonlinear oscillator. This model immediately refers to a large class of mesoscopic vibrational systems, from nanomechanical resonators to quantum cavity modes to Josephson junctions. The scaling behavior of the switching rates will be outlined and a comparison with the experiment will be made.