Whilst the majority of individuals infected with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the causative pathogen of COVID-19, experience mild to moderate symptoms, approximately 20% develop severe respiratory complications that may progress to acute respiratory distress syndrome, pulmonary failure and death. To date, single cell and high-throughput systems based analyses of the peripheral and pulmonary immune responses to SARS-CoV-2 suggest that a hyperactive and dysregulated immune response underpins the development of severe disease, with a prominent role assigned to neutrophils. Characterised in part by robust generation of neutrophil extracellular traps (NETs), the presence of immature, immunosuppressive and activated neutrophil subsets in the circulation, and neutrophilic infiltrates in the lung, a granulocytic signature is emerging as a defining feature of severe COVID-19. Furthermore, an assessment of the number, maturity status and/or function of circulating neutrophils at the time of hospital admission has shown promise as a prognostic tool for the early identification of patients at risk of clinical deterioration. Here, by summarising the results of studies that have examined the peripheral and pulmonary immune response to SARS-CoV-2, we provide a comprehensive overview of the changes that occur in the composition, phenotype and function of the neutrophil pool in COVID-19 patients of differing disease severities and discuss potential mediators of SARS-CoV-2-induced neutrophil dysfunction. With few specific treatments currently approved for COVID-19, we conclude the review by discussing whether neutrophils represent a potential therapeutic target for the treatment of patients with severe COVID-19.