Recent research has shown that there are a number of atoms and atomic ions that can bind a positron. The number of atoms known to be capable of binding a positron has expanded enormously in recent years, with Li, He(S-3(e)), Be, Na, Mg, Ca; Cu, Zn, Sr, Ag and Cd all capable of binding a positron. The structure of these systems is largely determined by the competition between the positron and the nucleus to bind the loosely bound valence electrons. Some systems, such as e(+)Li and e(+)Na, can be best described as a Ps cluster orbiting a charged Li+ or Na+ core, while others such as e(+)Be consist of a positron orbiting a polarized Be atom. In addition, a number of atoms (Li, C, O, F, Na, Cl, K, Cl, Cu, Br) can bind positronium and a few syst...