Little is understood about the brain, the mind and their relationships. However, rapid technical advances in brain-imaging devices such as positron emission tomography (PET), functional magnetic resonance imaging, EEG and EMG have increased the capabilities for visualizing the working brain, and uncovering the cerebral areas participating in the realization of cognitive tasks, and progress in cognitive science has led to a better understanding of the functional architecture of mental abilities. There is, therefore, considerable potential for achieving a greater understanding of the relationships between cognition and cerebral structures through brain-imaging studies of mental functions. However, these studies are confronted with a series of difficulties related to the assumptions that govern their application, the constraints imposed by these techniques on the design of cognitive experiments, the complexities inherent in establishing relations between cognition and anatomy through physiology, and to the interpretation of patterns of cerebral activation. In this article, potential difficulties are described drawing essentially on examples from PET studies of cognitive functions. Whereas a bright future lies ahead for the study of human brain mapping, many problems still have to be overcome and solved in order to exploit the full potential of new brain-imaging techniques.