Abstract.High molecular weight polymer solutions have a powerful tendency to deposit adsorbed layers when exposed to even mildly attractive surfaces. The equilibrium properties of these dense interfacial layers have been extensively studied theoretically. A large body of experimental evidence, however, indicates that non-equilibrium effects are dominant whenever monomer-surface sticking energies are somewhat larger than kT , a common case. Polymer relaxation kinetics within the layer are then severely retarded, leading to non-equilibrium layers whose structure and dynamics depend on adsorption kinetics and layer ageing. Here we review experimental and theoretical work exploring these non-equilibrium effects, with emphasis on recent developments. The discussion addresses the structure and dynamics in non-equilibrium polymer layers adsorbed from dilute polymer solutions and from polymer melts and more concentrated solutions. Two distinct classes of behaviour arise, depending on whether physisorption or chemisorption is involved. A given adsorbed chain belonging to the layer has a certain fraction of its monomers bound to the surface, f , and the remainder belonging to loops making bulk excursions. A natural classification scheme for layers adsorbed from solution is the distribution of single chain f values, P (f ), which may hold the key to quantifying the degree of irreversibility in adsorbed polymer layers. Here we calculate P (f ) for equilibrium layers; we find its form is very different to the theoretical P (f ) for non-equilibrium layers which are predicted to have infinitely many statistical classes of chain. Experimental measurements of P (f ) are compared to these theoretical predictions.