This will be a survey of recent constructions of a new class of partial differential equations arising from the study of the period mappings of certain CY and general complete intersection families in a complex manifold X.These PDE systems,which we call tautological systems,are important in that they often determine the period integrals of those families of varieties and that they are amenable to explicit descriptions.We give one in terms of representation theory,in case X is a projective homogeneous manifold.