Totally Skew Embeddings of Manifolds

A totally skew embedding of a manifold in Euclidean space is an example of an embedding with extra regularity conditions. For totally skew embeddings, we require the tangent spaces at all distinct points on the manifold to be pairwise skew. I will give a brief history of this problem, discuss some of the older results as well as more recent ones, and explain some connections with other areas of topology/geometry.