Cryptosporidiosis is a water- and food-borne zoonotic disease caused by the protozoon parasite of the genus Cryptosporidium. C. hominis and C. parvum are the main two species causing infections in humans and animals. The disease can be transmitted by the fecal–oral route as well as the respiratory route. The infective stage (sporulated oocysts) is resistant to different disinfectants including chlorine. Currently, no effective therapeutic drugs or vaccines are available to treat and control Cryptosporidium infection. To prevent cryptosporidiosis in humans and animals, we need to understand better how the disease is spread and transmitted, and how to interrupt its transmission cycle. This review focuses on understanding cryptosporidiosis, including its infective stage, pathogenesis, life cycle, genomics, epidemiology, previous outbreaks, source of the infection, transmission dynamics, host spectrum, risk factors and high-risk groups, the disease in animals and humans, diagnosis, treatment and control, and the prospect of an effective anti-Cryptosporidium vaccine. It also focuses on the role of the One Health approach in managing cryptosporidiosis at the animal–human–environmental interface. The summarized data in this review will help to tackle future Cryptosporidium infections in humans and animals and reduce the disease occurrence.