Leishmania is a genus of protozoan parasites that are transmitted by the bite of phlebotomine sandflies and give rise to a range of diseases (collectively known as leishmaniases) that affect over 150 million people worldwide. Cellular immune mechanisms have a major role in the control of infections with all Leishmania spp. However, as discussed in this Review, recent evidence suggests that each host–pathogen combination evokes different solutions to the problems of parasite establishment, survival and persistence. Understanding the extent of this diversity will be increasingly important in ensuring the development of broadly applicable vaccines, drugs and immunotherapeutic interventions.