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The Tutte polynomial is a fundamental invariant associated to a graph,matroid, vector arrangement, or hyperplane arrangement. This short surveyfocuses on some of the most important results on Tutte polynomials ofhyperplane arrangements. We show that many enumerative, algebraic, geometric,and topological invariants of a hyperplane arrangement can be expressed interms of its Tutte polynomial. We also show that, even if one is onlyinterested in computing the Tutte polynomial of a graph or a matroid, thetheory of hyperplane arrangements provides a powerful finite field method forthis computation.

Tutte polynomials of hyperplane arrangements and the finite field method