The idea that perception in humans relies on some form of probabilistic computations has become very popular over the last decades. It has been extremely difficult however to characterize the extent and the nature of the probabilistic representations and operations that are manipulated by neural populations in the human cortex. Several theoretical works suggest that probabilistic representations are present from low-level sensory areas to high-level areas. According to this view, the neural dynamics implements some forms of probabilistic message passing (i.e. neural sampling, probabilistic population coding, etc.) which solves the problem of perceptual inference. Here I will present recent experimental evidence that human and non-human primate perception implements some form of message passing. I will first review findings showing probabilistic integration of sensory evidence across space and time in primate visual cortex. Second, I will show that the confidence reports in a hierarchical task reveal that uncertainty is represented both at lower and higher levels, in a way that is consistent with probabilistic message passing both from lower to higher and from higher to lower representations. Finally, I will present behavioral and neural evidence that human perception takes into account pairwise correlations in sequences of sensory samples in agreement with the message passing hypothesis, and against standard accounts such as accumulation of sensory evidence or predictive coding.