  The Tutte polynomial is a fundamental invariant associated to a graph,
matroid, vector arrangement, or hyperplane arrangement. This short survey
focuses on some of the most important results on Tutte polynomials of
hyperplane arrangements. We show that many enumerative, algebraic, geometric,
and topological invariants of a hyperplane arrangement can be expressed in
terms of its Tutte polynomial. We also show that, even if one is only
interested in computing the Tutte polynomial of a graph or a matroid, the
theory of hyperplane arrangements provides a powerful finite field method for
this computation.
