Mounting evidence suggests that 'core object recognition,' the ability to rapidly recognize objects despite substantial appearance variation, is solved in the brain via a cascade of reflexive, largely feedforward computations that culminate in a powerful neuronal representation in the inferior temporal cortex. However, the algorithm that produces this solution remains poorly understood. Here we review evidence ranging from individual neurons and neuronal populations to behavior and computational models. We propose that understanding this algorithm will require using neuronal and psychophysical data to sift through many computational models, each based on building blocks of small, canonical subnetworks with a common functional goal.