Water electrolysis driven by renewable energy can produce clean hydrogen, but its efficiency remains low, in part because of slow kinetics at the anode for the oxygen evolution reaction (OER). Learning from the most active catalysts for the OER, iridium oxides, would be the key to the development and establishment of design guidelines for active and stable OER catalysts. This article reviews in situ or operando spectroscopic and advanced computational studies in the past decade concerning the OER over iridium oxide for both the oxidation of water molecules and hydroxide ions. By collectively reviewing the reported findings, we illustrate the plausible OER catalytic cycles including the dissolution of iridium during the reaction, which at the same time disclosed discrepancies in the proposed mechanisms. Such discrepancies are thought to originate from variations in the experimental conditions employed in those studies, calling for comprehensive and systematic in situ or operando studies in the future. Toward the end, we discuss a recent approach for improving the activity and stability of OER catalysts.