The electronic properties of the n =1 and n =2 members of the iridate Ruddelsden-Popper series Sr 2n+1 Ir n O 3n+1 have recently garnered a considerable amount of interest, primarily due to claims of their manifestation of a novel J eff =1/2 Mott insulating phase. Exploring what phases emerge upon doping this Mott insulating state and the degree to which strong spin-orbit coupling can drive the appearance of new electronic behavior in these compounds are now active areas of investigation; however, currently, the properties of even the undoped systems remain surprisingly poorly understood. Here, I present the results of our group’s recent studies exploring the electronic properties of the bilayer insulating iridate Sr 3 Ir 2 O 7 . Through a combined charge transport, magnetization, and neutron scattering study, we argue for a picture of a complex ground state with multiple electronic order parameters. How the ground state evolves upon tuning the system from a 5d-electron antiferromagnetic insulator toward its 4d-electron cousin Sr 3 Ru 2 O 7 , where the ground state is that of a nearly ferromagnetic Fermi liquid, will also be discussed.