  We prove several superrigidity results for isometric actions on metric spaces
satisfying some convexity properties. First, we extend some recent theorems of
N. Monod on uniform and certain non-uniform irreducible lattices in products of
locally compact groups. Second, we include the proof of an unpublished result
on commensurability superrigidity due to Margulis. The proofs rely on certain
notions of harmonic maps and the study of their existence, uniqueness, and
continuity.
