Enteropathogenic porcine epidemic diarrhea virus (PEDV) and porcine deltacoronavirus (PDCoV), members of the coronavirus family, account for the majority of lethal watery diarrhea in neonatal pigs in the past decade. These two viruses pose significant economic and public health burdens, even as both continue to emerge and reemerge worldwide. The ability to evade, circumvent or subvert the host’s first line of defense, namely the innate immune system, is the key determinant for pathogen virulence, survival, and the establishment of successful infection. Unfortunately, we have only started to unravel the underlying viral mechanisms used to manipulate host innate immune responses. In this review, we gather current knowledge concerning the interplay between these viruses and components of host innate immunity, focusing on type I interferon induction and signaling in particular, and the mechanisms by which virus-encoded gene products antagonize and subvert host innate immune responses. Finally, we provide some perspectives on the advantages gained from a better understanding of host-pathogen interactions. This includes their implications for the future development of PEDV and PDCoV vaccines and how we can further our knowledge of the molecular mechanisms underlying virus pathogenesis, virulence, and host coevolution.