Advances in ion-source, accelerator and beam-cooling technology have made it possible to produce high-quality beams of atomic ions in arbitrary charged states as well as molecular and cluster ions that are internally cold. Ion beams of low emittance and narrow momentum spread are obtained in a new generation of ion storage-cooler rings dedicated to atomic and molecular physics. The long storage times (similar to 5 s less than or similar to tau less than or similar to days) allow the study of very slow processes occurring in charged (positive and negative) atoms, molecules and clusters. Interactions of ions with electrons and/or photons can be studied by merging the stored ion beam with electron and laser beams. The physics of storage rings spans particles having a charge-to-mass ratio ranging from <0.002 (C-60(+) and C-70(+)) to 0.4-1.0 (H+, D+, He2+,...,U92+) and collision processes ranging from <1 meV to similar to 70 GeV. It incorporates, in addition to atomic and molecular physics, tests of fundamental physics theories and atomic physics bordering on nuclear and chemical physics. This exciting development concerning ion storage rings has taken place within the last five to six years.