Object perception depends on shape processing in the ventral visual pathway, which in monkeys culminates in inferotemporal cortex (IT). Here we provide a description of fundamental quantitative principles governing neural selectivity for complex shape in IT. By measuring responses to large, parametric sets of two-dimensional (2D) silhouette shapes, we found that neurons in posterior IT (Brodmann's areas TEO and posterior TE) integrate information about multiple contour elements (straight and curved edge fragments of the type represented in lower-level areas) using both linear and nonlinear mechanisms. This results in complex, distributed response patterns that cannot be characterized solely in terms of example stimuli. We explained these response patterns with tuning functions in multidimensional shape space and accurately predicted neural responses to the widely varying shapes in our stimulus set. Integration of contour element information in earlier stages of IT represents an important step in the transformation from low-level shape signals to complex object representation.