The classical arguments favouring a genetic basis of ageing are reviewed emphasizing the questions that remain unanswered. Genes cannot be the sole genetic determinants of ageing. Mendel's paradigm cannot anymore explain all the results recently obtained. Different aspects of the organization of the genome must also play a role in ageing. The functions of the largest part of the human genome remain unknown. Moreover the different genetic theories of ageing are based on natural selection. However, other paradigms are being proposed that can complement or replace Darwin's paradigm. They are based on the spontaneous organization of complex systems. They must be considered in the reappraisal of the ageing phenomenon.