Continuum Damage Mechanics (C.D.M.) has developed continuously since the early works of Kachanov and Rabotnov. It constitutes a practical tool to take into account the various damaging processes in materials and structures at a macroscopic continuum level. The main basic features of C.D.M. are considered in the first part together with its present capabilities, including damage definitions and measures, and its incorporation into a thermodynamic general framework. Practical damage growth equations will be reviewed in the second part of the paper.