In this seminar I will report on an ongoing research project (together with G. Canevari, M. Snarski and M. Veneroni) focused on Nematic Shells. These are the datum of a two dimensional compact surface (without boundary, for simplicity) coated with a thin film of nematic liquid crystal. I will introduce and discuss the analytic features of an elastic surface energy recently introduced by G. Napoli and L. Verger. A particular attention will be given to the relations between the functional setting and the topology of the surface and, possibly, of the boundary conditions. Among the others, I will discuss the basic theory of the gradient flow of the energy for Nematic Shells of genus one. When restricting to the axisymmetric torus, I will present some finer properties of the minimizers together with some numerical simulations.