  We classify totally geodesic submanifolds of the real Stiefel manifolds of
orthogonal two-frames. We also classify polar actions on these Stiefel
manifolds, specifically, we prove that the orbits of polar actions are lifts of
polar actions on the corresponding Grassmannian. In the case of
cohomogeneity-one actions we are able to obtain a classification for all real,
complex and quaternionic Stiefel manifolds of $k$-frames.
