Solvent evaporation from homopolymer and heteropolymer films along with the interdiffusion of solvent into these films are studied by molecular dynamics simulations. Due to the high viscosity of polymer melts, in many cases polymer films are made by first dissolving the polymer in a low viscosity solvent, spreading the solution on a substrate and subsequently evaporating the solvent. Here we study the last part of this process, namely the evaporation of solvent from a polymer film. As the solvent evaporates, the polymer density at the film/vapour interface is found to increase sharply, creating a polymer density gradient which acts as a barrier for further solvent evaporation. For both homopolymer and heteropolymer films, the rate of solvent evaporation is found to decrease exponentially as a function of time. For multiblock co-polymer films the resulting domain structure is found to be strongly affected by the relative stiffness of the two blocks. The reverse process, namely the interdiffusion of solvent into a polymer film, is also studied. For homopolymer films the weight gain by the film scales as t^1/2, which is expected for Fickian diffusion. The diffusivity D(c) determined from the one-dimensional Fick's diffusion equation agrees well with that calculated from the corrected diffusion constant using the Darken equation. Far above the polymer glass transition temperature, D(c) is nearly independent of concentration. However, as the temperature decreases D(c) is found to depend strongly on the state of the polymer and is related to the shape of the solvent concentration profile. Finally, the swelling of a multiblock copolymer film in which the stiffer block is below its glass transition temperature is also studied. While the solvent swells only the softer block of the copolymer, the weight gain by the film remains Fickian.