The Ruddlesden-Popper phases Sr_n+1Ir_nO_3n+1 (n = 1, 2, and ∞) have been intensively studied, and exhibit many novel behaviors and ground states driven by a rare interplay between strong spin-orbit and Coulomb interactions. One key empirical trend is that most iridates are antiferromagnetic insulators, contrary to conventional wisdom. The spin-orbit-coupled Mott state does not always closely track the magnetic state in iridates. Often, chemical doping can effectively induce a metallic state. Defying expectations, Sr₂IrO₄, which is the prototypical spin-orbit-coupled Mott insulator, does not become superconducting upon electron doping, but remains insulating under applied pressures extending into the Mbar range, highlighting the extraordinary susceptibility to the lattice degrees of freedom, which is at the heart of the physics driving the iridates.