The perovskite iridate Srn+1IrnO3n+1 realizes an interesting analogue to the cuprate high Tc superconductor. When electron-doped, the single-layer Sr2IrO4 is shown to manifest a pseudogap phase and possibly d-wave superconductivity. Using second harmonic generation rotational anisotropy, we show that near the antiferromagnetic transition there exists a magnetic multipolar order that breaks inversion symmetry in hole-doped Sr2IrO4. One candidate for this order is the loop current order that is predicted to exist in the pseudogap region of cuprate. In bilayer Sr3Ir2O7, electron-doping has been found to induce an insulator-to-metal transition in addition to a structural phase transition at low temperature. There has been no prior experimental evidence of electronic instabilities in the bilayer system. Using time-resolved optical reflectivity, we detect a charge-density-wave-like instability in metallic samples of electron-doped Sr3Ir2O7. The absence of signatures of a new spatial periodicity from diffraction, scanning tunnelling and photoemission based probes suggests an unconventional and possibly short-ranged nature of this density wave order.