  This paper is a survey of the subject of variations of Hodge structure (VHS)
considered as exterior differential systems (EDS). We review developments over
the last twenty-six years, with an emphasis on some key examples. In the
penultimate section we present some new results on the characteristic
cohomology of a homogeneous Pfaffian system. In the last section we discuss how
the integrability conditions of an EDS affect the expected dimension of an
integral submanifold. The paper ends with some speculation on EDS and Hodge
conjecture for Calabi-Yau manifolds.
