Glassy dynamics under nanoscale confinement have been subject of under intense debate in soft matter physics in the last 20 years. Scientific impetus in the field was provided by the increasing employment of glasses confined at the nanoscale. Furthermore, investigation of confined glasses may deliver information of the still unsolved problem of the glass transition. Within this context, the present chapter critically discusses the experimental findings in the field. Special attention is devoted to literature dealing with polymers under 1-D confinement, that is, thin polymer film. Results on different confinement geometries, such as polymer nanocomposites and nanospheres, are discussed as well. In discussing these results, we emphasize how the out-of-equilibrium dynamics, that is, the glass transition temperature (T g ) and the spontaneous evolution towards equilibrium in the so-called physical aging regime, is in numerous cases decoupled from the equilibrium dynamics, namely the rate of spontaneous fluctuations in the glass former. In particular, arguments based exclusively on the modification of the rate of spontaneous fluctuations in confinement are not able to provide a comprehensive description of the deviation of the T g and the rate of physical aging. In the search for the factors affecting the out-of-equilibrium dynamics in confinement, we show solid experimental evidence that this is mainly determined by the amount of free interface. In this sense the crucial role of irreversible chain adsorption is highlighted. Finally a framework, based on free volume holes diffusion (FVHD), to describe the entire phenomenology of glassy dynamics in confinement is reviewed. This is able to catch the enhancement of the out-of-equilibrium dynamics, that is, the T g depression and the speed-up of physical aging in confinement, with no need to invoke any acceleration of the rate of spontaneous fluctuations of the polymer.