Ambiguous figures that may take on the appearance of two or more distinct forms have fascinated philosophers and psychologists for generations. Recently, several laboratories have studied the neuronal basis of perceptual appearance at the level of single neurons in the cerebral cortex. Experiments that integrate neuronal recording with analyses based on sensory detection theory reveal a remarkable degree of specificity in these neuronal responses. The new challenges are to understand how cognitive processes, such as attention and memory, interact with perception to generate these neuronal signals.