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Giant anomalous events may occur in systems characterized by many waves, with extremely high amplitude waves appearing with a probability much higher than expected for a random dynamics. Such rare, and giant, events are known to occur on the ocean surface and have been named, in that context, “rogue waves”. We present here some recent experimental results on the statistical properties of giant optical waves, or “optical rogue waves”, observed in spatially extended optical systems. We will present the main statistical features of such extreme events, then, based on both a linear and a nonlinear experiment, we will outline a way enabling us to identify two key ingredients at the origin of optical rogue waves, namely, granularity, that is, a minimal size of the individual light spots, and inhomogeneity, that is, clustering of the light spots into separate domains with different average intensities. In the linear experiment we measure also the statistics of the waiting times between successive rogue waves and we show that it follows a log-Poisson distribution, which is characteristics of event separation observed in cooperative, complex systems and in such different fields as geophysics and biology.