Recognition memory is widely viewed as consisting of two components, recollection and familiarity, which have been proposed to be dependent on the hippocampus and the adjacent perirhinal cortex, respectively. Here, we propose an alternative perspective: we suggest that the methods traditionally used to separate recollection from familiarity instead separate strong memories from weak memories. A review of work with humans, monkeys and rodents finds evidence for familiarity signals (as well as recollection signals) in the hippocampus and recollection signals (as well as familiarity signals) in the perirhinal cortex. We also indicate ways in which the functions of the medial temporal lobe structures are different, and suggest that these structures work together in a cooperative and complementary way.