A while ago I heard that there was no known triangulation of the Grassmannian of 3-planes in 6-space.
To believe a statement like that, you have to be a little bit ungenerous about what you mean by "known." For instance if something is cut out by some polynomial equations and inequalities in R^n, I think there is an algorithm for writing down a simplicial complex homeomorphic to it. But it is not a very satisfying one, maybe even computationally infeasible in some sense.
Real projective space is easy to triangulate. Complex projective space is of the form (torus) x (simplex) divided by a simple equivalence relation on the boundary, so probably a triangulation can be cooked up from there. And there's a beautiful 9-vertex triangulation of CP^2 which is probably not of this form:
The real Grassmannian of 2-planes in n-space could probably be triangulated by refining the partition by oriented matroids. But for 3-planes and higher, this partition is too crazy.
What are some other triangulations of Grassmannians? Is the claim about 3-planes in 6-space accurate? Is there a reference for 2-planes in n-space?