Immunological memory - the ability to 'remember' previously encountered pathogens and respond faster on re-exposure - is a central feature of the immune response of vertebrates. We outline how mathematical models have contributed to our understanding of CD8(+) T-cell memory. Together with experimental data, models have helped to quantitatively describe and to further our understanding of both the generation of memory after infection with a pathogen and the maintenance of this memory throughout the life of an individual.