We review the theoretical studies of atomic resonances in three-body systems involving positrons. These works employ a method of complex-coordinate rotation. Investigations on resonances in positron-hydrogen scattering below various hydrogen and positronium thresholds are discussed, as well as resonances in e^+ -He^+ scattering. Furthermore, resonances in electron-positronium scattering will also be reviewed. The theoretical results for doubly-excited states of Ps^- reveal the supermultiplete structures of such an ion, and its tri-atomic molecular characters in analogy to an XYX molecule.