The problem of the cognitive penetrability of perception pertains to whether perceptual processing may be impacted by higher-order cognitive processes. It may be understood in a twofold sense: 1) whether what a perceptual system computes may be altered in a way that is semantically coherent to one’s cognitive states; 2) whether perceptual experience may be influenced by cognitive processes. It has been argued that the cognitive penetrability problem is not scientifically tractable since we have no direct access to other persons’ (...) subjective experiences and, therefore, we have to rely on their reports, which are mediated by higher-order processes (e.g., judgments). In this paper, I analyze the scope of methods harnessed in contemporary work on the penetrability of perception, focusing particularly on methods from experimental psychology and neuroscience. Among them, I indicate the most promising techniques and paradigms, as well as those that are inadequate to successfully tackling the problem. I also discuss experimental results which unequivocally suggest direct influences on perception which have not been addressed to date by supporters of the view that perception is impenetrable. I also describe the predictive processing theory of cognition, focusing on how it contributes to our understanding of cognitive penetrability, and discuss scientific results validating the theory. In conclusion, converging empirical evidence seems to suggest that perception is cognitively penetrable and we seem to be at the dawn of the ultimate solution of the problem. (shrink)