The Coronavirus Disease 2019 (COVID-19) pandemic has drawn closer attention than ever before to the problems of the immunopathology of human diseases, many of which have been reflected when studying immune-mediated inflammatory rheumatic diseases (IIRDs). The hyperimmune response called a cytokine storm, the pathogenetic subtypes of which include hemophagocytic lymphohistiocytosis, macrophage activation syndrome, and cytokine release syndrome, is among the most serious complications of IIRDs or treatment for malignant neoplasms and may be a stage of COVID-19 progression. A premium is placed to interleukin-6 (IL-6) in the spectrum of cytokines involved in the pathogenesis of the cytokine storm syndrome. The clinical introduction of monoclonal antibodies (mAbs) that inhibit the activity of this cytokine (tocilizumab, sarilumab, etc.) is one of the major advances in the treatment of IIRDs and critical conditions within the cytokine storm syndrome in COVID-19. The review discusses data on the clinical and prognostic value of IL-6 and the effectiveness of anti-IL-6 receptor and anti-IL-6 mAbs, as well as prospects for personalized therapy of the cytokine storm syndrome in COVID-19.