The visual system uses sequences of selective glimpses to objects to support goal-directed behavior, but how is this attention control learned? Here we present an encoder–decoder model inspired by the interacting bottom-up and top-down visual pathways making up the recognition-attention system in the brain. At every iteration, a new glimpse is taken from the image and is processed through the “what” encoder, a hierarchy of feedforward, recurrent, and capsule layers, to obtain an object-centric (object-file) representation. This representation feeds to the “where” decoder, where the evolving recurrent representation provides top-down attentional modulation to plan subsequent glimpses and impact routing in the encoder. We demonstrate how the attention mechanism significantly improves the accuracy of classifying highly overlapping digits. In a visual reasoning task requiring comparison of two objects, our model achieves near-perfect accuracy and significantly outperforms larger models in generalizing to unseen stimuli. Our work demonstrates the benefits of object-based attention mechanisms taking sequential glimpses of objects.