Human noroviruses (HuNoVs) are increasingly becoming the main cause of transmissible gastroenteritis worldwide, with hundreds of thousands of deaths recorded annually. Yet, decades after their discovery, there is still no effective treatment or vaccine. Efforts aimed at developing vaccines or treatment will benefit from a greater understanding of norovirus-host interactions, including the host response to infection. In this review, we provide a concise overview of the evidence establishing the significance of type I and type III interferon (IFN) responses in the restriction of noroviruses. We also critically examine our current understanding of the molecular mechanisms of IFN induction in norovirus-infected cells, and outline the diverse strategies deployed by noroviruses to supress and/or avoid host IFN responses. It is our hope that this review will facilitate further discussion and increase interest in this area.