This is an exposition of recent results—obtained in joint work with Andrzej Derdzinski—on essentially conformally symmetric (ECS) manifolds, that is, those pseudo-Riemannian manifolds with parallel Weyl curvature which are not locally symmetric or conformally flat. In the 1970s, Roter proved that while Riemannian ECS manifolds do not exist, pseudo-Riemannian ones do exist in all dimensions \(n\geq 4\) and realize all indefinite metric signatures. The local structure of ECS manifolds is known, and every ECS manifold carries a distinguished null parallel distribution \(\mathcal {D}\) , whose rank is always equal to 1 or 2. We review basic facts about ECS manifolds, briefly discuss the construction of compact examples, and outline the proof of a topological structure result: outside of the locally homogeneous case and up to a double covering, every compact rank-one ECS manifold is a bundle over \(\mathbb {S}^1\) whose fibers are the leaves of \(\mathcal {D}^\perp \) . Finally, we mention some classification results for compact rank-one ECS manifolds.