Understanding the T cell response to SARS-CoV-2 is critical to vaccine development, epidemiological surveillance, and control strategies for this disease. This review provides data from studies of the immune response in coronavirus infections. It describes general mechanisms of immunity, its T cell components, and presents a detailed scheme of the T cell response in SARS-CoV-2 infection, including from the standpoint of determining the most promising targets for assessing its level. In addition, we reviewed studies investigating post-vaccination immunity in the development of vaccines against COVID-19. This review also includes the peculiarities of immunity in different age and gender groups, and in the presence of a number of factors, for example, comorbidity or disease severity. This study summarizes the most informative methods for assessing the immune response to SARS-CoV-2 infection.