The ventral visual pathway transforms retinal images into neural representations that support object understanding, including exquisite appreciation of precise 2D pattern shape and 3D volumetric shape. We articulate a framework for understanding the goals of this transformation and how they are achieved by neural coding at successive ventral pathway stages. The critical goals are (a) radical compression to make shape information communicable across axonal bundles and storable in memory, (b) explicit coding to make shape information easily readable by the rest of the brain and thus accessible for cognition and behavioral control, and (c) representational stability to maintain consistent perception across highly variable viewing conditions. We describe how each transformational step in ventral pathway vision serves one or more of these goals. This three-goal framework unifies discoveries about ventral shape processing into a neural explanation for our remarkable experience of shape as a vivid, richly detailed aspect of the natural world.