Inferences made about objects via vision, such as rapid and accurate categorization, are core to primate cognition despite the algorithmic challenge posed by varying viewpoints and scenes. Until recently, the brain mechanisms that support these capabilities were deeply mysterious. However, over the past decade, this scientific mystery has been illuminated by the discovery and development of brain-inspired, image-computable, artificial neural network (ANN) systems that rival primates in these behavioral feats. Apart from fundamentally changing the landscape of artificial intelligence, modified versions of these ANN systems are the current leading scientific hypotheses of an integrated set of mechanisms in the primate ventral visual stream that support core object recognition. What separates brain-mapped versions of these systems from prior conceptual models is that they are sensory computable, mechanistic, anatomically referenced, and testable (SMART). In this article, we review and provide perspective on the brain mechanisms addressed by the current leading SMART models. We review their empirical brain and behavioral alignment successes and failures, discuss the next frontiers for an even more accurate mechanistic understanding, and outline the likely applications.