Cell death by apoptosis is a major cellular response in the control of tissue homeostasis and as a defense mechanism in the case of cellular aggression such as an infection. Cell self-destruction is part of antiviral responses, aimed at limiting the spread of a virus. Although it may contribute to the deleterious effects in infectious pathology, apoptosis remains a key mechanism for viral clearance and the resolution of infection. The control mechanisms of cell death processes by viruses have been extensively studied. Apoptosis can be triggered by different viral determinants through different pathways as a result of virally induced cell stresses and innate immune responses. Zika virus (ZIKV) induces Zika disease in humans, which has caused severe neurological forms, birth defects, and microcephaly in newborns during the last epidemics. ZIKV also surprised by revealing an ability to persist in the genital tract and in semen, thus being sexually transmitted. Mechanisms of diverting antiviral responses such as the interferon response, the role of cytopathic effects and apoptosis in the etiology of the disease have been widely studied and debated. In this review, we examined the interplay between ZIKV infection of different cell types and apoptosis and how the virus deals with this cellular response. We illustrate a duality in the effects of ZIKV-controlled apoptosis, depending on whether it occurs too early or too late, respectively, in neuropathogenesis, or in long-term viral persistence. We further discuss a prospective role for apoptosis in ZIKV-related therapies, and the use of ZIKV as an oncolytic agent.