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In this review we provide an organized summary of the theoretical andcomputational results which are available for polymers subject to spatial ortopological constraints. Because of the interdisciplinary character of thetopic, we provide an accessible, non-specialist introduction to the maintopological concepts, polymer models, and theoretical/computational methodsused to investigate dense and entangled polymer systems. The main body of ourreview deals with: (i) the effect that spatial confinement has on theequilibrium topological entanglement of one or more polymer chains and (ii) themetric and entropic properties of polymer chains with fixed topological state.These problems have important technological applications and implications forthe life-sciences. Both aspects, especially the latter, are amply covered. Anumber of selected open problems are finally highlighted.

Polymers with spatial or topological constraints: theoretical and computational results