Aging of the immune system involves functional changes in individual cell populations, in hematopoietic tissues and at the systemic level. They are mediated by factors produced by circulating cells, niche cells, and at the systemic level. Age-related alterations in the microenvironment of the bone marrow and thymus cause a decrease in the production of naive immune cells and functional immunodeficiencies. Another result of aging and reduced tissue immune surveillance is the accumulation of senescent cells. Some viral infections deplete adaptive immune cells, increasing the risk of autoimmune and immunodeficiency conditions, leading to a general degradation in the specificity and effectiveness of the immune system in old age. During the COVID-19 pandemic, the state-of-the-art application of mass spectrometry, multichannel flow cytometry, and single-cell genetic analysis have provided vast data on the mechanisms of aging of the immune system. These data require systematic analysis and functional verification. In addition, the prediction of age-related complications is a priority task of modern medicine in the context of the increase in the aged population and the risk of premature death during epidemics. In this review, based on the latest data, we discuss the mechanisms of immune aging and highlight some cellular markers as indicators of age-related immune disbalance that increase the risk of senile diseases and infectious complications.