Seeing movement drives survival. It results from an uncertain interplay between evolution and experience, making it hard to isolate the drivers of computational architectures found in brains. Here we seek insight into motion perception using a neural network (‘MotionNet’) trained on moving images to classify velocity. The network recapitulates key properties of (a) motion direction and (b) speed processing in biological brains, and we use it to derive, and test, understanding of motion (mis)perception at the computational-, neural-, and perceptual-levels. We show that diverse motion characteristics are largely explained by the statistical structure of natural images, rather than motion per se. First, we show how neural and perceptual biases for particular motion directions can result from the orientation structure of natural images. Second, we demonstrate an interrelation between speed and direction preferences in (macaque) MT neurons that can be explained by image autocorrelation. Third, we show that natural image statistics mean that speed and image contrast are related quantities. Finally, using behavioural tests (humans, box sexes), we show that it is apparently knowledge of the speed-contrast association that accounts for motion illusions, rather than the distribution of movements in the environment (the ‘slow world’ prior) as premised by Bayesian accounts. Together this provides an exposition of motion speed and direction estimation, and produces concrete predictions for future neurophysiological experiments. More broadly we demonstrate the conceptual value of marrying artificial systems with biological characterisation, moving beyond ‘black box’ reproduction of an architecture to advance understanding of complex systems like the brain.