As Grassmannians
A more modern classification (Huang & Leung 2011) uniformly classifies the Riemannian symmetric spaces, both compact and non-compact, via a Freudenthal magic square construction. The irreducible compact Riemannian symmetric spaces are, up to finite covers, either a compact simple Lie group, a Grassmannian, a Lagrangian Grassmannian, or a double Lagrangian Grassmannian of subspaces of for normed division algebras A and B. A similar construction produces the irreducible non-compact Riemannian symmetric spaces.
Read more about this topic: Symmetric Space, Classification of Riemannian Symmetric Spaces