Object perception seems effortless to us, but it depends on intensive neural processing across multiple stages in ventral pathway visual cortex. Shape information at the retinal level is hopelessly complex, variable and implicit. The ventral pathway must somehow transform retinal signals into much more compact, stable and explicit representations of object shape. Recent findings highlight key aspects of this transformation: higher-order contour derivatives, structural representation in object-based coordinates, composite shape tuning dimensions, and long-term storage of object knowledge. These coding principles could help to explain our remarkable ability to perceive, distinguish, remember and understand a virtual infinity of objects.