Severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) is responsible for the current COVID-19 pandemic. SARS-CoV-2 is characterized by an important capacity to circumvent the innate immune response. The early interferon (IFN) response is necessary to establish a robust antiviral state. However, this response is weak and delayed in COVID-19 patients, along with massive pro-inflammatory cytokine production. This dysregulated innate immune response contributes to pathogenicity and in some individuals leads to a critical state. Characterizing the interplay between viral factors and host innate immunity is crucial to better understand how to manage the disease. Moreover, the constant emergence of new SARS-CoV-2 variants challenges the efficacy of existing vaccines. Thus, to control this virus and readjust the antiviral therapy currently used to treat COVID-19, studies should constantly be re-evaluated to further decipher the mechanisms leading to SARS-CoV-2 pathogenesis. Regarding the role of the IFN response in SARS-CoV-2 infection, in this review we summarize the mechanisms by which SARS-CoV-2 evades innate immune recognition. More specifically, we explain how this virus inhibits IFN signaling pathways (IFN-I/IFN-III) and controls interferon-stimulated gene (ISG) expression. We also discuss the development and use of IFNs and potential drugs controlling the innate immune response to SARS-CoV-2, helping to clear the infection.