Cryptosporidium is increasingly recognized as one of the major causes of moderate to severe diarrhoea in developing countries. With treatment options limited, control relies on knowledge of the biology and transmission of the members of the genus responsible for disease. Currently, 26 species are recognized as valid on the basis of morphological, biological and molecular data. Of the nearly 20 Cryptosporidium species and genotypes that have been reported in humans, Cryptosporidium hominis and Cryptosporidium parvum are responsible for the majority of infections. Livestock, particularly cattle, are one of the most important reservoirs of zoonotic infections. Domesticated and wild animals can each be infected with several Cryptosporidium species or genotypes that have only a narrow host range and therefore have no major public health significance. Recent advances in next-generation sequencing techniques will significantly improve our understanding of the taxonomy and transmission of Cryptosporidium species, and the investigation of outbreaks and monitoring of emerging and virulent subtypes. Important research gaps remain including a lack of subtyping tools for many Cryptosporidium species of public and veterinary health importance, and poor understanding of the genetic determinants of host specificity of Cryptosporidium species and impact of climate change on the transmission of Cryptosporidium.