  Period domains, the classifying spaces for (pure, polarized) Hodge
structures, and more generally Mumford-Tate domains, arise as open
$G_{\mathbb{R}}$--orbits in flag varieties $G/P$. We investigate
Hodge--theoretic aspects of the geometry and representation theory associated
with these flag varieties. In particular, we relate the Griffiths--Yukawa
coupling to the variety of lines on $G/P$ (under a minimal homogeneous
embedding), construct a large class of polarized $G_{\mathbb{R}}$--orbits in
$G/P$, and compute the associated Hodge--theoretic boundary components. An
emphasis is placed throughout on adjoint flag varieties and the corresponding
families of Hodge structures of levels two and four.
