Calculations have demonstrated that eleven neutral atoms can bind positrons, while many more can bind positronium. This is a short review of recent progress made in understanding some of the underlying mechanisms. The emphasis here being on configuration interaction calculations with excited state configurations. These have demonstrated the existence of a P-2(o) excited state of e(+)Ca, which consists predominantly of a positronium cluster orbiting the Ca+ ion in the L = 1 partial wave. Preliminary results are presented of excited state positron binding to a model alkali atom, where the excited P-1(o) states are stable over a limited region. Implications for the unnatural parity, S-2,4(o) states of PsH, LiPs, NaPs and KPs are also discussed. The e(+)Mg, e(+)Cu, e(+)Zn and e(+)Cd systems show a lack of a P-2(o) excited state, each instead possessing a low-energy p-wave shape resonance of varying strength.