Recognition memory relies on two processes: (i) identification and (ii) judgement concerning prior occurrence. A system centred on perirhinal cortex appears to be responsible for judgement of prior occurrence based on discrimination of the familiarity of stimuli or their recency of occurrence; in contrast, a hippocampal system probably supplies information concerning the episodic, contextual aspects of recognition memory. This review chiefly concerns the perirhinal system and, in particular, neurones that signal the prior occurrence of stimuli by a decrease in response. Details concerning such decremental responses are given and it is argued that such responses in perirhinal cortex are adequate for and central to discrimination of stimulus familiarity and recency in a wide range of situations. Information is given of similar types of neuronal responses in anatomically related brain regions and what may be deduced about the operation of the recognition memory system. The possibility is discussed that the neuronal responses that signal information concerning the recent occurrence of stimuli may contribute to repetition priming as well as recognition memory. Other described changes in the activity of individual neurones such as response enhancements, or sustained (delay) activity may allow solution of specialised forms of recognition memory tasks where relatively short-term working memory is adequate. Implications of the multi-faceted nature of recognition memory for the interpretation of results are emphasised. Unsolved problems and avenues for future experimentation, including determining the nature of possible underlying synaptic plastic changes, are discussed.