The Tutte polynomial is a classical invariant of graphs (and matroids). I will explain how to extend it to hypergraphs (and polymatroids), state some properties that the extension retains, and describe a newly emerging phenomenon: the interior polynomials of a hypergraph and its transpose agree. This result, whose proof is joint work with A. Postnikov, is intimately related to the root polytope of a bipartite graph.