The epidemic due to severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) infection has been spreading globally, raising increasing concerns. This public health emergency has triggered a race to find medications to improve the prognosis of this disease. There is currently great interest in drug repositioning to manage SARS-CoV-2 infection, that is, the evaluation of the potential benefits of a drug that has already been proven safe and effective in humans for other approved indications. As interleukin-6 (IL-6) acts as a key driver of the inflammation associated with coronavirus disease 2019 (COVID-19), IL-6 and IL-6 receptor (IL-6R) inhibition appear to be promising targets for the treatment of COVID-19 patients. It is important to critically analyze the available evidence concerning the use of the available anti-IL-6 (siltuximab) and anti-IL-6R (tocilizumab and sarilumab) agents in COVID-19 patients, in terms of both benefit and risk. In this review, the pathogenesis of the cytokine storm induced by COVID-19, the role of IL-6 in this cytokine storm, the rationale for the use of anti-IL-6 agents, and key information on potential benefits and safety monitoring of these biologicals in COVID-19 patients is discussed.