Relaxation phenomena in three different classical and quantum systems are investigated. First, the role of multiplicative and additive noise in a classical metastable system is analyzed. The mean lifetime of the metastable state shows a nonmonotonic behavior with a maximum as a function of both the additive and multiplicative noise intensities. In the second system, the simultaneous action of thermal and non-Gaussian noise on the dynamics of an overdamped point Josephson junction is studied. The effect of a Levy noise generated by a Cauchy-Lorentz distribution on the mean lifetime of the superconductive metastable state, in the presence of a periodic driving, is investigated. We find resonant activation and noise enhanced stability in the presence of Levy noise. Finally, the time evolution of a quantum particle moving in a metastable potential and interacting with a thermal reservoir is analyzed. Within the Caldeira-Legget model and the Feynman-Vernon functional approach, we obtain the time evolution of the population distributions in the position eigenstates of the particle, for different values of the thermal bath coupling strength.