Technical Abstract: The protozoan parasites belonging to the genus Cryptosporidium infect all classes of vertebrate animals. Of the sixteen valid species and nearly forty genotypes, three species are responsible for the majority of economic losses to livestock and morbidity and mortality to humans. This chapter summarizes the history of the scientific milestones, the taxonomic problems, the need for molecular identification of species and genotypes, host ranges of species and genotypes, life cycle stages and their morphology at the electron microscope level, methods of transmission, and means of prevention, control, and treatment. This is the first chapter of a completely revised and updated book entitled Cryptosporidium and Cryptosporidiosis, 2nd edition by R. Fayer and L. Xiao.