The article provides an overview of the taxonomy of *Cryptosporidium*, a genus of apicomplexan parasites that infect a wide range of vertebrate hosts, including humans. The authors discuss the historical perspective of *Cryptosporidium* taxonomy, the species concept, and the criteria for naming new species. They highlight the importance of host-parasite coevolution and host adaptation in understanding the taxonomy of *Cryptosporidium*. The article also addresses the public health implications of *Cryptosporidium* taxonomy, including the identity of species in humans and animals, infection sources, and implications for the water industry. The authors emphasize the challenges in diagnosing and differentiating between *Cryptosporidium* species due to morphological similarities and the lack of clear diagnostic features. They review the molecular characterizations that have helped clarify the taxonomy and validate the existence of multiple species within each vertebrate class. The article concludes with a discussion on the valid species of *Cryptosporidium*, including those infecting mammals, birds, reptiles, and fish, and the ongoing efforts to identify and name new species.The article provides an overview of the taxonomy of *Cryptosporidium*, a genus of apicomplexan parasites that infect a wide range of vertebrate hosts, including humans. The authors discuss the historical perspective of *Cryptosporidium* taxonomy, the species concept, and the criteria for naming new species. They highlight the importance of host-parasite coevolution and host adaptation in understanding the taxonomy of *Cryptosporidium*. The article also addresses the public health implications of *Cryptosporidium* taxonomy, including the identity of species in humans and animals, infection sources, and implications for the water industry. The authors emphasize the challenges in diagnosing and differentiating between *Cryptosporidium* species due to morphological similarities and the lack of clear diagnostic features. They review the molecular characterizations that have helped clarify the taxonomy and validate the existence of multiple species within each vertebrate class. The article concludes with a discussion on the valid species of *Cryptosporidium*, including those infecting mammals, birds, reptiles, and fish, and the ongoing efforts to identify and name new species.