No sensory stimulus is an island unto itself; rather, it can only properly be interpreted in light of the stimuli that surround it in space and time. This can result in entertaining illusions and puzzling results in psychological and neurophysiological experiments. We concentrate on perhaps the best studied test case, namely orientation or tilt, which gives rise to the notorious tilt illusion and the adaptation tilt after-effect. We review the empirical literature and discuss the computational and statistical ideas that are battling to explain these conundrums, and thereby gain favour as more general accounts of cortical processing.