Several eigenvalue problems have been suggested to provide “target signatures” for inverse scattering problems. In particular, the relevant eigenvalue problems are those associated with the direct scattering problem that are accessible to measurement from a knowledge of the scattering data. In this talk I shall discuss five different sets of eigenvalues that can be used as target signatures for inverse electromagnetic scattering: 0) Scattering resonances, 1) eigenvalues of the electric far field operator, 2) transmission eigenvalues and 3) Stekloff eigenvalues and 4) modified transmission eigenvalues.