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 to symptoms relief, such as fever and rash, by administering antipyretics, anti-histamines, and fluids for dehydration. Nevertheless, lately, a great effort has been made to search for antiviral candidates using different approaches and methodologies, ranging from repurposing of specific compounds with known antiviral activity to the screening of libraries and of natural compounds. The identified antiviral candidates include drugs targeting viral components (structural proteins and enzymes), as well as cellular ones. 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.