Virus infection of eukaryotes triggers cellular innate immune response, a major arm of which is the type I interferon (IFN) family of cytokines. Binding of IFN to cell surface receptors triggers a signaling cascade in which the signal transducer and activator of transcription 2 (STAT2) plays a key role, ultimately leading to an antiviral state of the cell. In retaliation, many viruses counteract the immune response, often by the destruction and/or inactivation of STAT2, promoted by specific viral proteins that do not possess protease activities of their own. This review offers a summary of viral mechanisms of STAT2 subversion with emphasis on degradation. Some viruses also destroy STAT1, another major member of the STAT family, but most viruses are selective in targeting either STAT2 or STAT1. Interestingly, degradation of STAT2 by a few viruses requires the presence of both STAT proteins. Available evidence suggests a mechanism in which multiple sites and domains of STAT2 are required for engagement and degradation by a multi-subunit degradative complex, comprising viral and cellular proteins, including the ubiquitin–proteasomal system. However, the exact molecular nature of this complex and the alternative degradation mechanisms remain largely unknown, as critically presented here with prospective directions of future study.