We describe a quantitative theory to account for the computations performed by the feedforward path of the ventral stream of visual cortex and the local circuits implementing them. We show that a model instantiating the theory is capable of performing recognition on datasets of complex images at the level of human observers in rapid categorization tasks. We also show that the theory is consistent with (and in some case has predicted) several properties of neurons in V1, V4, IT and PFC. The theory seems sufficiently comprehensive, detailed and satisfactory to represent an interesting challenge for physiologists and modelers: either disprove its basic features or propose alternative theories of equivalent scope. The theory suggests a number of open questions for visual physiology and psychophysics.