An overview of the structure and stability properties of superheavy nuclei obtained from a microscopic approach employing the Gogny effective nucleon--nucleon interaction is presented. Shell gaps, fission barriers and stability against \alpha -decay are discussed and compared with experimental data and other theoretical approaches. In particular, a few \alpha -decay chains of odd nuclides observed in recent experiments are examined.

PACS numbers: 21.10, 21.60, 27.90.+b, 23.60.+e