Since late 2019, the new SARS-CoV-2 virus belonging to the family has been responsible for COVID-19 pandemic, a severe acute respiratory syndrome. Several antiviral therapies, mostly derived from previous epidemics, were initially repurposed to fight this not rarely life-threatening respiratory illness. Among them, however, the only specific antibody-based therapy available against SARS-CoV-2 infection during the first year of the pandemic was represented by COVID-19 convalescent plasma (CCP). CCP, collected from recovered individuals, contains high levels of polyclonal antibodies of different subclasses able to neutralize SARS-CoV-2 infection. Tens of randomized controlled trials have been conducted during the last three years of the pandemic to evaluate the safety and the clinical efficacy of CCP in both hospitalized and ambulatory COVID-19 patients, whose main results will be summarized in this narrative review. In addition, we will present the current knowledge on the development of anti-SARS-CoV-2 hyperimmune polyclonal immunoglobulins.