  Two interesting questions in algebraic geometry are: (i) how can a smooth
projective varieties degenerate? and (ii) given two such degenerations, when
can we say that one is "more singular/degenerate" than the other? Schmid's
Nilpotent Orbit Theorem yields Hodge-theoretic analogs of these questions, and
the Hodge-theoretic answers in turn provide insight into the motivating
algebro-geometric questions, sometimes with applications to the study of
moduli. Recently the Hodge-theoretic questions have been completely answered.
This is an expository survey of that work.
