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Due to coexisting electron-correlation and the spin-orbit interaction, 5d transition-metal oxides, e.g., complex iridates, have received a great deal of attention. However, our understanding of the system advances rather slowly owing to limited experimental approaches. In this colloquium, I will discuss our recent research on layered (2D) iridate thin-films of A₂IrO₄ (A = Ba, Sr, Ca). Note that the Ba₂IrO₄ and Ca₂IrO₄ phases do not exist in nature, yet their thermodynamically meta-stable phases can be synthesized using an epitaxy-stabilizing technique. Moreover, I will show artificial heterostructures of one-dimensional (1D) iridates consisting of linear Ir-O-Ir stripes. This approach of investigating artificial 1D systems opens a new avenue to explore low-dimensional quantum physics. Based on our recent experimental investigations of transport, optical spectroscopy, and resonant inelastic x-ray scattering, I will discuss our current understanding of the complex iridates and their topological properties due to coexisting strong electron-correlation and spin-orbit interaction.