I will give a (biased) survey on the role and importance of totally geodesic submanifolds, particularly in negative curvature. The goal will be to start with some broad strokes motivation in terms of differential geometry and symmetry, to move through older work where totally geodesic manifolds play a key role as a tool and then reach recent work of my own with various coauthors where finiteness results were proven.  This includes joint work with Bader, Elliott Smith, Filip, Lafont, Lowe, Miller, and Stover.  Elliott Smith and Miller were both UCSD undergrads.