In this paper we review molecular modeling investigations of polymer/layered-silicate intercalates, as model systems to explore polymers in nanoscopically confined spaces. The atomic-scale picture, as revealed by computer simulations, is presented in the context of salient results from a wide range of experimental techniques. This approach provides insights into how polymeric segmental dynamics are affected by severe geometric constraints. Focusing on intercalated systems, i.e. polystyrene (PS) in 2 nm wide slit-pores and polyethylene-oxide (PEO) in 1 nm wide slit-pores, a very rich picture for the segmental dynamics is unveiled, despite the topological constraints imposed by the confining solid surfaces. On a local scale, intercalated polymers exhibit a very wide distribution of segmental relaxation times (ranging from ultra-fast to ultra-slow, over a wide range of temperatures). In both cases (PS and PEO), the segmental relaxations originate from the confinement-induced local density variations. Additionally, where there exist special interactions between the polymer and the confining surfaces (e.g., PEO) more molecular mechanisms are identified.