Normal human somatic cells have strictly limited proliferative capacity and reach a state of senescence when it becomes exhausted. It is believed that senescence is a response to extensive and irreparable DNA injury, localized in telomeric and/or non-telomeric regions of the genome. Main cause of this damage is oxidative stress, increasing due to deteriorated function of mitochondria. Senescent cells accumulate in tissues during aging, which is causatively linked with the development of various pathologies in elderly individuals, including cancer. This paper, prepared exactly 50 years after Leonard Hayflick's discovery of the relationship between cellular senescence and organismal aging is aimed at presenting the current knowledge about molecular determinants of senescence, with particular emphasis paid to the role of oxidative stress, effectors of senescence at the level of cell cycle, markers of this phenomenon, and the effect of senescent cells on the development of certain age-related diseases.