  We introduce non-linear $\sigma$-models in the framework of noncommutative
geometry with special emphasis on models defined on the noncommutative torus.
We choose as target spaces the two point space and the circle and illustrate
some characteristic features of the corresponding $\sigma$-models. In
particular we construct a $\sigma$-model instanton with topological charge
equal to 1. We also define and investigate some properties of a noncommutative
analogue of the Wess-Zumino-Witten model.
