Harmonic maps of infinite energy

I will recall the standard existence and uniqueness theorems for harmonic maps from a Riemannian manifold to a space of non-positive curvature, and list a couple applications. I will then try to motivate the study of infinite energy harmonic maps, to which the standard theorems do not in general apply. By this time you will hopefully be delighted to learn that there are more recent existence and uniqueness theorems of Markovic, Benoit-Hulin, Tosic, and others that work also in the infinite energy setting. I will present recent work with Max Riestenberg which synthesizes, and further generalizes, these infinite-energy results.