Neurophysiological evidence is described showing that some neurons in the macaque inferior temporal visual cortex have responses that are invariant with respect to the position, size and view of faces and objects, and that these neurons show rapid processing and rapid learning. Which face or object is present is encoded using a distributed representation in which each neuron conveys independent information in its firing rate, with little information evident in the relative time of firing of different neurons. This ensemble encoding has the advantages of maximising the information in the representation useful for discrimination between stimuli using a simple weighted sum of the neuronal firing by the receiving neurons, generalisation and graceful degradation. These invariant representations are ideally suited to provide the inputs to brain regions such as the orbitofrontal cortex and amygdala that learn the reinforcement associations of an individual's face, for then the learning, and the appropriate social and emotional responses, generalise to other views of the same face. A theory is described of how such invariant representations may be produced in a hierarchically organised set of visual cortical areas with convergent connectivity. The theory proposes that neurons in these visual areas use a modified Hebb synaptic modification rule with a short-term memory trace to capture whatever can be captured at each stage that is invariant about objects as the objects change in retinal view, position, size and rotation. Another population of neurons in the cortex in the superior temporal sulcus encodes other aspects of faces such as face expression, eye gaze, face view and whether the head is moving. These neurons thus provide important additional inputs to parts of the brain such as the orbitofrontal cortex and amygdala that are involved in social communication and emotional behaviour. Outputs of these systems reach the amygdala, in which face-selective neurons are found, and also the orbitofrontal cortex, in which some neurons are tuned to face identity and others to face expression. In humans, activation of the orbitofrontal cortex is found when a change of face expression acts as a social signal that behaviour should change; and damage to the orbitofrontal cortex can impair face and voice expression identification, and also the reversal of emotional behaviour that normally occurs when reinforcers are reversed.