  Using the theory of $\Gamma$-convergence, we derive from three-dimensional
elasticity new one-dimensional models for non-Euclidean elastic ribbons, i.e.
ribbons exhibiting spontaneous curvature and twist. We apply the models to
shape-selection problems for thin films of nematic elastomers with twist and
splay-bend texture of the nematic director. For the former, we discuss the
possibility of helicoid-like shapes as an alternative to spiral ribbons.
