Interferons (IFNs) are crucial components of the cellular innate immune response to viral infections. The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has shown a remarkable capacity to suppress the host IFN production to benefit viral replication and spread. Thus far, of the 28 known virus-encoded proteins, 16 have been found to impair the host's innate immune system at various levels ranging from detection and signaling to transcriptional and post-transcriptional regulation of expression of the components of the cellular antiviral response. Additionally, there is evidence that the viral genome encodes non-protein-coding microRNA-like elements that could also target IFN-stimulated genes. In this brief review, we summarise the current state of knowledge regarding the factors and mechanisms by which SARS-CoV-2 impairs the production of IFNs and thereby dampens the host's innate antiviral immune response.