The Bernstein-Sato polynomial of a hypersurface is related to several concepts in commutative algebra. After an introduction to the general properties of this polynomial, we will focus on the case of hyperplane arrangements. We will discuss relations to Milnor fibers, to the intersection lattice of the arrangement, and the Jacobian ideal of the arrangement. We will also discuss new results, in the arrangement case, on the conjectured connection between the topological zeta function and the Bernstein-Sato polynomial.