The Grassmannian $G_n(\mathbb{R}^k)$ of n-planes in $\mathbb{R}^k$ has a CW-complex structure coming from the Schubert cell decomposition.

What is known about the attaching maps in this CW-complex structure?

I understand that a lot of work has been done to try to understand the answer to this question using things like Schubert calculus, Young diagrams, Steenrod operations, etc. I'd like to see some kind of collection of know results about the attaching maps and the specific techniques used to obtain those results.

I'm also interested in the case of the complex Grassmannians.