In late 2015, an increase in the number of infants born with microcephaly in poor communities in northeast Brazil prompted investigation of antenatal Zika infection as the cause. Zika now circulates in 69 countries, and has affected pregnancies of women in 29 countries. Public health officials, policymakers, and international organizations are considering interventions to address health consequences of the Zika epidemic. To date, public health responses have focused on mosquito vector eradication, sexual and reproductive health services, knowledge and technology including diagnostic test and vaccine development, and health system preparedness. We summarize responses to date and apply human rights and related principles including nondiscrimination, participation, the legal and policy context, and accountability to identify shortcomings and to offer suggestions for more equitable, effective, and sustainable Zika responses.