When we look at an image, its features are represented in our visual system in a highly distributed manner, calling for a mechanism that binds them into coherent object representations. There have been different proposals for the neuronal mechanisms that can mediate binding. One hypothesis is that binding is achieved by oscillations that synchronize neurons representing features of the same perceptual object. This view allows separate communication channels between different brain areas. Another hypothesis is that binding of features that are represented in different brain regions occurs when the neurons in these areas that respond to the same object simultaneously enhance their firing rate, which would correspond to directing object-based attention to these features. This review summarizes evidence in favor of and against these two hypotheses, examining the neuronal correlates of binding and assessing the time course of perceptual grouping. I conclude that enhanced neuronal firing rates bind features into coherent object representations, whereas oscillations and synchrony are unrelated to binding.