The Siegert (or Gamow) wave function associated with a resonance state is exponentially divergent at large distances from the scattering target. A complex absorbing potential (CAP) provides a computationally simple and efficient technique for calculating the complex Siegert energy of a resonance within a square-integrable basis. Some aspects of the associated complex symmetric eigenvalue problem will be addressed. Applications to the decay of inner-shell holes, to elastic electron-molecule scattering, and to multiphoton processes will be described.