Human and non-human primates excel at visual recognition tasks. The primate visual system exhibits a strong degree of selectivity while at the same time being robust to changes in the input image. We have developed a quantitative theory to account for the computations performed by the feedforward path in the ventral stream of the primate visual cortex. Here we review recent predictions by a model instantiating the theory about physiological observations in higher visual areas. We also show that the model can perform recognition tasks on datasets of complex natural images at a level comparable to psychophysical measurements on human observers during rapid categorization tasks. In sum, the evidence suggests that the theory may provide a framework to explain the first 100-150 ms of visual object recognition. The model also constitutes a vivid example of how computational models can interact with experimental observations in order to advance our understanding of a complex phenomenon. We conclude by suggesting a number of open questions, predictions, and specific experiments for visual physiology and psychophysics.