SynopsisThe simplest class of constraints on a polymer chain involves the other chains in a one-phase homogeneous system. One major unresolved issue in this area is the nature and importance of entanglements, particularly with regard to mechanical properties. Issues of particular importance are differences between inter-chain entanglements and chain-junction entanglements, their contributions at elastic equilibrium, and how they are affected by cross-linking in a state of strain or in solution. Some topological issues also arise in the area of sorption of linear and cyclic diluents into networks, and the ease of extracting the linear chains relative to extracting identical chains which had been present during the formation of the network. If the diluents present during the end linking procedure are cyclics, then some of them are permanently trapped by being threaded through with one or more linear chains prior to network formation. The amount trapped in this way depends very strongly on the size of the cyclic. The experimental trapping efficiencies can be satisfactorily explained using Monte Car10 simulations based on the standard rotational isomeric state model for the cyclic molecules.The multi-phase systems of greatest interest are those in which a polymeric phase is constrained by being absorbed onto a surface, or trapped within a second constraining phase, typically a hard porous ceramic. The former is illustrated by a thin film of polymer coated onto a surface with which it strongly interacts, and the latter by a polymer chain threading its way through the cavities of a zeolite or nanotube. Polymers themselves do not show the required degree of cooperation for such threading, but monomers do absorb into such cavities and can be polymerized to yield structures of this type. The hope is that such novel arrangements will have correspondingly novel physical properties. A second major part of this review therefore describes a number of recent studies of thin polymer films, and some attempts to prepare nanocomposites in which polymer chains thread through the cavities or channels of several types of inorganic material (specifically zeolites, galleries in clay-like materials, silica nanotubes, and mesoporous hexagonal