The iridates have become fertile ground for studies of new physics driven by spin-orbit coupling (SOC) that is comparable to the on-site Coulomb and other relevant  interactions.  This unique circumstance creates a delicate balance between interactions that drives complex magnetic and dielectric behaviors and exotic states seldom or never seen in other materials. A profound manifestation of this competition is the novel Jeff = 1/2 Mott state that was observed in the layered iridates with tetravalent Ir4+(5d5) ions. On the other hand, very little attention has been drawn to iridates having pentavalent Ir5+(5d4) ions, primarily because the strong SOC limit is expected to impose a nonmagnetic singlet ground state (Jeff  = 0). In this talk, we review the underlying physical properties of the iridates including perovskites, honeycomb lattices and double perovskites with pentavalent Ir5+ ions, and report results of our recent studies that emphasize spin-orbit-tuned ground states stabilized by chemical doping, application of pressure and magnetic field. In addition, we address the urgent question that the Jeff states may not survive in the presence of strong non-cubic crystal fields and/or exchange interactions.