The mechanisms of aging are described at the molecular, cell, tissue, and systemic levels. Primary age-dependent molecular lesions activate the cell stress response to compensate for the resulting defects, but the mechanisms that recover and maintain homeostasis are gradually deteriorated. When the amount of errors reaches a critical threshold in regulatory networks, a phase transition from health to disease occurs at the systemic level. The review considers the approaches to quantitative assessment of the aging process (biomarkers of aging) and promising interventions to slow down the aging process and to reduce the risk of age-dependent diseases.