CAT(0) geometry is a metric generalization of Riemannian non-positive curvature. One could wonder, in the context of closed manifolds, if this is a genuine generalization? Up to dimension three, every closed manifold supporting a CAT(0) metric also supports a Riemannian non-positively curved metric. But this is no longer true when the dimension is >3. I will give an overview of the various known constructions of “exotic” CAT(0) manifolds in higher dimensions, culminating in a sketch of some new high dimensional examples (joint work w/ Bakul Sathaye).