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