Neurons in early sensory cortex show weak but systematic correlations with perceptual decisions when trained animals perform at psychophysical threshold. These correlations are observed across repeated presentations of identical stimuli and cannot be explained by variation in external factors. The relationship between the activity of individual sensory neurons and the animal's behavioral choice means that even neurons in early sensory cortex carry information about an upcoming decision. This relationship, termed choice probability, may reflect the effect of fluctuations in neuronal firing rate on the animal's decision, but it can also reflect modulation of sensory responses by cognitive factors, or network properties such as variability that is shared among populations of neurons. Here, we review recent work clarifying the relationship among fluctuations in the responses of individual neurons, correlated variability, and behavior in a variety of tasks and cortical areas. We also discuss the possibility that choice probability may in part reflect the influence of cognitive factors on sensory neurons and explore the situations in which choice probability can be used to make inferences about the role of particular sensory neurons in the decision-making process.