Scattering poles is a classic topic in scattering theory and carries important physical information. They play critical roles in various scattering processes in quantum mechanics, acoustics, electromagnetics, and many other fields. The computation of scattering poles is challenging as the associated spectral problem is nonlinear and defined on the unbounded domain. We present some recent numerical investigations including the boundary integral method and FE DtN method. The parallel multistep spectral indicator method is employed to compute the eigenvalues of the resulting linear systems. Numerical examples demonstrate the effectiveness of our approach.