Immunosenescence and inflammaging in the aging process: age-related diseases or longevity?

•Immunosenescence represents a dynamic process describing the changes occurring in the innate and adaptive immune system with age.•Immunosenescence is considered an adaptive process that can remodel the immune system in response to many stimuli humans are exposed to during life.•Inflammaging represents an example of remodeling as the result of the imbalance between inflammatory and anti-inflammatory networks.•Centenarians, a model of successful aging, are characterized by an optimal balance between pro- and anti-inflammatory factors.•The adaptive mechanisms generated by immunosenescence and inflammaging determine the susceptibility to several diseases, including COVID-19.