This thesis is concerned with effects of geometrical confinement on dynamics in disordered materials in the nanoscopic range. Of particular interest is the dynamics around the liquid to glass transition. Two systems have been investigated: thin polymer films and polymer gels. The dynamics was examined over a broad range in time, 10-12 - 103 s, using photon correlation spectroscopy, dielectric spectroscopy and quasi-eleastic neutron scattering. The large scale structure of the gels was investigated using small angle neutron scattering. The effect of polymer chain confinement was examined for polystyrene films that are thinner than the equilibrium end-to-end distance of a single polymer chain. The experiments are the first study describing the form of the structural relaxations in thin free-standing polymer films. It shows that the relaxation becomes faster for thinner films, but the shape of the relaxation function remains similar to that of the bulk polymer. Cooperativity and confinement effects were also investigated in polymer gels systems consisting of propylene carbonate (PC) stabilized with poly(methyl methacrylate). The experiments reveal that the main structural relaxation of PC confined in the gel can be described by a simple cooperative model. An onset temperature for cooperative relaxations is identified to be located approximately 60 K above the glass transition temperature. Salt-doped polymer gel electrolytes are promising for application in electrochemical devices since they combine high ionic conductivity with mechanical stability. Experiments aiming at determining the molecular basis for the ion conduction mechanism in such systems are presented. A complex relaxational behavior was observed with at least three relaxation processes. It is concluded that there is a close relation between the diffusion of the solvent and the ionic conductivity