Zika virus (ZIKV), a mosquito-borne flavivirus, was an almost neglected pathogen until its introduction in the Americas in 2015, where it has been responsible for a threat to global health, causing a great social and sanitary alarm due to its increased virulence, rapid spread, and an association with severe neurological and ophthalmological complications. Currently, no specific antiviral therapy against ZIKV is available, and treatments are palliative and mainly directed toward the relief of symptoms, such as fever and rash, by administering antipyretics, anti-histamines, and fluids for dehydration. Nevertheless, lately, search for antivirals has been a major aim in ZIKV investigations. To do so, screening of libraries from different sources, testing of natural compounds, and repurposing of drugs with known antiviral activity have allowed the identification of several antiviral candidates directed to both viral (structural proteins and enzymes) and cellular elements. Here, we present an updated review of current knowledge about anti-ZIKV strategies, focusing on host-directed antivirals as a realistic alternative to combat ZIKV infection.