Abstract: One-cusped hyperbolic 2- and 3-manifolds of finite volume are quite easy to build, thanks to the uniformization theorem and work of Thurston, respectively. A one-cusped hyperbolic 4-manifold wasn't known until work of Kolpakov and Martelli about a decade ago, and it is unknown if one-cusped hyperbolic manifolds - or more generally negatively curved locally symmetric manifolds - exist in higher dimensions. The other 4-D negatively curved locally symmetric space is complex hyperbolic 2-space, which has constant holomorphic curvature -1. Martin Deraux recently found the first one-cusped complex hyperbolic 2-manifolds using computer experiment. I will describe more recent work where Deraux and I give an explicit topological construction using finite groups acting on products of Riemann surfaces and a uniformization hammer due to Tian and Yau.