During the current pandemic, the vast majority of COVID-19 patients experienced mild symptoms, but some had a potentially fatal aberrant hyperinflammatory immune reaction characterized by high levels of IL-6 and other cytokines. Modulation of this immune reaction has proven to be the only method of reducing mortality in severe and critical COVID-19. The anti-inflammatory drug baricitinib (Olumiant) has recently been strongly recommended by the WHO for use in COVID-19 patients because it reduces the risk of progressive disease and death. It is a Janus Kinase (JAK) 1/2 inhibitor approved for rheumatoid arthritis which was suggested in early 2020 as a treatment for COVID-19. In this review the AI-assisted identification of baricitinib, its antiviral and anti-inflammatory properties, and efficacy in clinical trials are discussed and compared with those of other immune modulators including glucocorticoids, IL-6 and IL-1 receptor blockers and other JAK inhibitors. Baricitinib inhibits both virus infection and cytokine signalling and is not only important for COVID-19 management but is “non-immunological”, and so should remain effective if new SARS-CoV-2 variants escape immune control. The repurposing of baricitinib is an example of how advanced artificial intelligence (AI) can quickly identify new drug candidates that have clinical benefit in previously unsuspected therapeutic areas.