Zika Virus (ZIKV) is a positive-strand RNA virus that can lead to Guillain-Barré syndrome or encephalitis in some individuals and hence presents a serious public health risk. Since the first outbreak of ZIKV in Brazil in 2015, no effective clinical inhibitors have been developed, making the development of effective ZIKV drugs an urgent issue that needs to be addressed. ZIKV belongs to the Flaviviridae family, and its structure includes three structural proteins, namely, capsular (C), premembrane (prM), and envelope (E) proteins, as well as seven nonstructural proteins, namely, NS1, NS2A, NS2B, NS3, NS4A, NS4B, and NS5. To provide a reference for the development of future ZIKV drugs, this paper reviews the structure of the ZIKV based on recent literature reports, analyzes the potential therapeutic targets of various proteins, and proposes feasible drug design strategies. Additionally, this paper reviews and classifies the latest research progress on several protease inhibitors, such as E protein inhibitors, NS2B-NS3 inhibitors, and NS5 inhibitors, so that researchers can quickly understand the current status of development and the interconnections among these inhibitors.