When polymers are confined in a narrow gap to a thickness comparable to the size of the molecule, new dynamic behavior emerges. The effective shear moduli are enhanced compared with the bulk, relaxation times are prolonged and nonlinear responses set in at lower shear rates. Key experimental findings discussed include static surface forces, linear shear dynamic moduli and nonlinear shear dynamic moduli, with special attention given to polymer melts and tethered block copolymers. Future areas of opportunity in this field are emphasized.