The ongoing Zika virus (ZIKV) epidemic and unexpected clinical outcomes, including Guillain-Barré syndrome and birth defects, has brought an urgent need for animal models. We evaluated infection and pathogenesis with contemporary and historical ZIKV strains in immunocompetent mice and mice lacking components of the antiviral response. Four- to six-week-old Irf3^−/− Irf5^−/− Irf7^−/− triple knockout mice, which produce little interferon α/β, and mice lacking the interferon receptor (Ifnar1^−/−) developed neurological disease and succumbed to ZIKV infection, whereas single Irf3^−/−, Irf5^−/−, and Mavs^−/− knockout mice exhibited no overt illness. Ifnar1^−/− mice sustained high viral loads in the brain and spinal cord, consistent with evidence that ZIKV causes neurodevelopmental defects in human fetuses. The testes of Ifnar1^−/− mice had the highest viral loads, which is relevant to sexual transmission of ZIKV. This model of ZIKV pathogenesis will be valuable for evaluating vaccines and therapeutics as well as understanding disease pathogenesis.