We present the MAC network, a novel fully differentiable neural network architecture, designed to facilitate explicit and expressive reasoning. MAC moves away from monolithic black-box neural architectures towards a design that encourages both transparency and versatility. The model approaches problems by decomposing them into a series of attention-based reasoning steps, each performed by a novel recurrent Memory, Attention, and Composition (MAC) cell that maintains a separation between control and memory. By stringing the cells together and imposing structural constraints that regulate their interaction, MAC effectively learns to perform iterative reasoning processes that are directly inferred from the data in an end-to-end approach. We demonstrate the model's strength, robustness and interpretability on the challenging CLEVR dataset for visual reasoning, achieving a new state-of-the-art 98.9% accuracy, halving the error rate of the previous best model. More importantly, we show that the model is computationally-efficient and data-efficient, in particular requiring 5x less data than existing models to achieve strong results.