Alzheimer’s disease is one of the most common age-related neurodegenerative disorders. The main theory of Alzheimer’s disease progress is the amyloid-β cascade hypothesis. However, the initial mechanisms of insoluble forms of amyloid-β formation and hyperphosphorylated tau protein in neurons remain unclear. One of the factors, which might play a key role in senile plaques and tau fibrils generation due to Alzheimer’s disease, is inflammaging, i.e., systemic chronic low-grade age-related inflammation. The activation of the proinflammatory cell phenotype is observed during aging, which might be one of the pivotal mechanisms for the development of chronic inflammatory diseases, e.g., atherosclerosis, metabolic syndrome, type 2 diabetes mellitus, and Alzheimer’s disease. This review discusses the role of the inflammatory processes in developing neurodegeneration, activated during physiological aging and due to various diseases such as atherosclerosis, obesity, type 2 diabetes mellitus, and depressive disorders.