With his famous paper on phi motion, Wertheimer (1912) launched Gestalt psychology, arguing that the whole is different from the sum of the parts. In fact, wholes were considered primary in perceptual experience, even determining what the parts are. Gestalt claims about global precedence and configural superiority are difficult to reconcile with what we now know about the visual brain, with a hierarchy from lower areas processing smaller parts of the visual field and higher areas responding to combinations of these parts in ways that are gradually more invariant to low-level changes to the input and corresponding more closely to perceptual experience. What exactly are the relationships between parts and wholes then? Are wholes constructed from combinations of the parts? If so, to what extent are the combinations additive, what does superadditivity really mean, and how does it arise along the visual hierarchy? How much of the combination process occurs in incremental feedforward iterations or horizontal connections and at what stage does feedback from higher areas kick in? What happens to the representation of the lower-level parts when the higher-level wholes are perceived? Do they become enhanced or suppressed ("explained away")? Or, are wholes occurring before the parts, as argued by Gestalt psychologists? But what does this global precedence really mean in terms of what happens where in the brain? Does the primacy of the whole only account for consciously perceived figures or objects, and are the more elementary parts still combined somehow during an unconscious step-wise processing stage? A century later, tools are available that were not at the Gestaltists’ disposal to address these questions.