  This paper is a survey of our work based on the stratified Morse theory of
Goresky and MacPherson. First we discuss the Morse theory of Euclidean space
stratified by an arrangement. This is used to show that the complement of a
complex hyperplane arrangement admits a minimal cell decomposition. Next we
review the construction of a cochain complex whose cohomology computes the
local system cohomology of the complement of a complex hyperplane arrangement.
Then we present results on the Gauss-Manin connection for the moduli space of
arrangements of a fixed combinatorial type in rank one local system cohomology.
