The intersection lattice of a hyperplane arrangement encodes the combinatorial data of how the hyperplanes intersect. Mnev's Universality Theorem suggests that the moduli space M(L) of hyperplane arrangements with fixed intersection lattice L can be arbitrarily complicated; indeed, it is even difficult to compute its dimension in general. Using Schubert Calculus, both the dimension D = dim M(L) and the degree of an embedding of the moduli space into a product of projective spaces can be computed when the arrangements are generic or cones over generic arrangements. Here the degree turns out to be the number of arrangements with intersection lattice L passing through D points in general position. This is joint work with Max Wakefield and our student, Tom Paul.