This chapter reviews the recent experiments involving the dynamics of polymer films with thickness comparable to the gyration radius of the polymer, which overwhelmingly show that their glass transition temperature, T g , depends on the film thickness and can sometimes differ significant from that of the bulk. The greatest mystery is the onset film thickness of this phenomenon being ~50 nm, much larger than the typical cooperativity size (~3 nm) of glass transition. While the sliding chain model [De Gennes, Eur. Phys. J. E (2000)] can qualitatively explain the results of the high molecular weight (M w ) freely-standing films, it fails to account for those of the low-M w freely-standing films and the supported films. For the latter two, at least two theories, i.e., the percolation theory [Long et al., ibid (2001)] and surface capillary wave theory [Herminghaus et al., ibid (2001)] have been proposed that can account for the observed thickness dependence of thin film T g . However, experimental data available at this time do not allow the theories to be distinguished. We briefly outline the physical ideas of these theories, and delineate how dynamical measurements of nanometer thick films may provide important insights about the problem.