This short review is focused on enzymatic properties of human ATP-dependent RNA helicase DDX3 and the development of antiviral and anticancer drugs targeting cellular helicases. DDX3 belongs to the DEAD-box proteins, a large family of RNA helicases that participate in all aspects of cellular processes, such as cell cycle progression, apoptosis, innate immune response, viral replication, and tumorigenesis. DDX3 has a variety of functions in the life cycle of different viruses. DDX3 helicase is required to facilitate both the Rev-mediated export of unspliced/partially spliced human immunodeficiency virus (HIV) RNA from nucleus and Tat-dependent translation of viral genes. DDX3 silencing blocks the replication of HIV, HCV, and some other viruses. On the other hand, DDX displays antiviral effect against Dengue virus and hepatitis B virus through the stimulation of interferon beta production. The role of DDX3 in different types of cancer is rather controversial. DDX3 acts as an oncogene in one type of cancer, but demonstrates tumor suppressor properties in other types. The human DDX3 helicase is now considered as a new attractive target for the development of novel pharmaceutical drugs. The most interesting inhibitors of DDX3 helicase and the mechanisms of their actions as antiviral or anticancer drugs are discussed in this short review.