We review in these lecture notes some of our recent work on mod- elling the response of nematic elastomers to applied mechanical loads and/or to electric fields, both in the static and in the dynamic regime. Our aim is to compare theoretical results based on mathematical anal- ysis and on numerical simulations with the available experimental evidence, in order to examine critically the various recent accom- plishments, and some challenging problems that remain open. Ne- matic elastomers combine the electro-optical properties and rotational degrees of freedom of nematic liquid crystals with the mechanical propeties and translational degrees of freedom of entropic rubbery solids. The rich behavior they exhibit, the interesting applications they seem to make possible, the breadth and depth of recent break- throughs at the experimental, theoretical, and computational level make nematic elastomers an exciting model system for advanced re- search in mechanics.
