How the processing of signals carried by sensory neurons supports perceptual decisions is a long-standing question in neuroscience. The ability to record neuronal activity in awake animals while they perform psychophysical tasks near threshold has been a key advance in studying these questions. Trial-to-trial correlations between the activity of sensory neurons and the decisions reported by animals (‘choice probabilities’), even when measured across repeated presentations of an identical stimulus provide insights into this problem. But understanding the sources of such co-variability between sensory neurons and behavior has proven more difficult than it initially appeared. Below, we discuss our current understanding of what gives rise to these correlations.