Topological insulators are materials, which are conducting at their edges, though not in the bulk. Their characteristic physical properties are reflected by an index, associated to the Hamiltonian. By a general principle, known as bulk-edge duality, the index can be defined either in terms of the bulk or the edge Hamiltonian. Among various ways of establishing that duality as a theorem, one is by scattering theory, and in fact by Levinson's theorem.