Coronavirus disease 2019 (COVID-19), the current pandemic disease, is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infection. Type I and III interferons (IFNs) are innate cytokines that are important in the first-line defense against viruses. Similar to many other viruses, SARS-CoV-2 has evolved mechanisms for evading the antiviral effects of type I and III IFNs at multiple levels, including the induction of IFN expression and cellular responses to IFNs. In this review, we describe the innate sensing mechanisms of SARS-CoV-2 and the mechanisms used by SARS-CoV-2 to evade type I and III IFN responses. We also discuss contradictory reports regarding impaired and robust type I IFN responses in patients with severe COVID-19. Finally, we discuss how delayed but exaggerated type I IFN responses can exacerbate inflammation and contribute to the severe progression of COVID-19.