Consider an arrangement of linear hyperplanes integral with respect to a given lattice. The lattice gives rise to a torus and the arrangement to a subdivision of the torus. We are interested in the combinatorics of this subdivision. We will describe questions and results for particular lattices associated to root systems and arrangements associated to graphs. This is joint work in progress with Swee Hong Chan.Consider an arrangement of linear hyperplanes integral with respect to a given lattice. The lattice gives rise to a torus and the arrangement to a subdivision of the torus. We are interested in the combinatorics of this subdivision. We will describe questions and results for particular lattices associated to root systems and arrangements associated to graphs. This is joint work in progress with Swee Hong Chan.