To use sensory information efficiently to make judgments and guide action in the world, the brain must represent and use information about uncertainty in its computations for perception and action. Bayesian methods have proven successful in building computational theories for perception and sensorimotor control, and psychophysics is providing a growing body of evidence that human perceptual computations are "Bayes' optimal". This leads to the "Bayesian coding hypothesis": that the brain represents sensory information probabilistically, in the form of probability distributions. Several computational schemes have recently been proposed for how this might be achieved in populations of neurons. Neurophysiological data on the hypothesis, however, is almost non-existent. A major challenge for neuroscientists is to test these ideas experimentally, and so determine whether and how neurons code information about sensory uncertainty.