Abstract: We discuss harmonic maps into NPC (non-positively curved) spaces and conditions when one can prove that such a map is totally geodesic or even constant. In the case the harmonic map is equivariant with respect to a representation of the fundamental group of the domain space to the isometry group of a NPC space, one can in this way deduce the rigidity of the representation. This research is motivated by the study of representations of lattices in non-Archimedian groups in connection with Margulis superrigidity.