Perception is often described as probabilistic inference requiring an internal representation of uncertainty. However, it is unknown whether uncertainty is represented in a task-dependent manner, solely at the level of decisions, or in a fully Bayesian manner, across the entire perceptual pathway. To address this question, we first codify and evaluate the possible strategies the brain might use to represent uncertainty, and highlight the normative advantages of fully Bayesian representations. In such representations, uncertainty information is explicitly represented at all stages of processing, including early sensory areas, allowing for flexible and efficient computations in a wide variety of situations. Next, we critically review neural and behavioral evidence about the representation of uncertainty in the brain agreeing with fully Bayesian representations. We argue that sufficient behavioral evidence for fully Bayesian representations is lacking and suggest experimental approaches for demonstrating the existence of multivariate posterior distributions along the perceptual pathway.