Cryptosporidium parvum is an apicomplexan parasite that infects the intestinal epithelium of humans and livestock animals worldwide. Cryptosporidiosis is a leading cause of diarrheal-related deaths in young children and a major cause of economic loss in cattle operations. The disease is especially dangerous to infants and immunocompromised individuals, for which there is no effective treatment or vaccination. As human-to-human, animal-to-animal and animal-to-human transmission play a role in cryptosporidiosis disease ecology, a holistic ‘One Health’ approach is required for disease control. Upon infection, the host’s innate immune response restricts parasite growth and initiates the adaptive immune response, which is necessary for parasite clearance and recovery. The innate immune response involves a complex communicative interplay between epithelial and specialized innate immune cells. Traditional models have been used to study innate immune responses to C. parvum but cannot fully recapitulate natural host-pathogen interactions. Recent shifts to human and bovine organoid cultures are enabling deeper understanding of host-specific innate immunity response to infection. This review examines recent advances and highlights research gaps in our understanding of the host-specific innate immune response to C. parvum . Furthermore, we discuss evolving research models used in the field and potential developments on the horizon.