We have simulated the photodynamics of azobenzene by means of the Surface Hopping method. We have considered both the trans -> cis and the cis -> trans processes, caused by excitation in the n -> pi* band (S-1 state). To bring out the solvent effects on the excited state dynamics, we have run simulations in four different environments: in vacuo, in n-hexane, in methanol, and in ethylene glycol. Our simulations reproduce very well the measured quantum yields and the time dependence of the intensity and anisotropy of the transient fluorescence. Both the photoisomerization and the S-1 -> S-0 internal conversion require the torsion of the N=N double bond, but the N-C bond rotations and the NNC bending vibrations also play a role. In the trans -> cis photoconversion the N=N torsional motion and the excited state decay are delayed by increasing the solvent viscosity, while the cis -> trans processes are less affected. The analysis of the simulation results allows the experimental observations to be explained in detail, and in particular the counterintuitive increase of the trans -> cis quantum yield with viscosity, as well as the relationship between the excited state dynamics and the solvent effects on the fluorescence lifetimes and depolarization.