The 2D O(N) non-linear sigma models are exactly solvable theories and, on the lattice, they have many applications from statistical mechanics to QCD toy models. In this talk, I will consider a particular generalization of the O(N) model, i.e. the non-linear sigma model on the supersphere. The global symmetry group of this model – the OSp(N+2M|2M) supergroup – mixes bosonic and fermionic degrees of freedom, hence the sigma model can be thought of as a toy model for string worldsheet theories with target space supersymmetry. In this talk, I will describe the non-linear sigma model on the supersphere, its discretization on the lattice, its renormalization properties, and the relation between this model and its non-supersymmetric equivalent. I will also present our strategy for numerical simulations and some preliminary numerical results.