Over the past few years, Sr2IrO4, a single-layer member of the Ruddlesden-Popper series iridates, has received much attention as a close analog of cuprate high-temperature superconductors. Although there is not yet firm evidence for superconductivity, a remarkable range of cuprate phenomenology has been reproduced in electron-and hole-doped iridates including pseudogaps, Fermi arcs, and d-wave gaps. Furthermore, many symmetry-breaking orders reminiscent of those decorating the cuprate phase diagram have been reported using various experimental probes. We discuss how the electronic structures of Sr2IrO4 through strong spin-orbit coupling leads to the low-energy physics that had long been unique to cuprates, what the similarities and differences between cuprates and iridates are, and how these advance the field of high-temperature superconductivity by isolating essential ingredients of superconductivity from a rich array of phenomena that surround it. Finally, we comment on the prospect of finding a new high-temperature superconductor based on the iridate series.