The importance of the DNA-damage repair mechanisms comes from the fact that any chemical modification to the DNA molecule, no matter how small it is, very often causes cell death and sometimes it can produce mutations whose biological effects are unpredictable. Taking into account that in the last decade great advances have been reported for the understanding of these mechanisms, and this knowledge can be essential to reach the control of the mutagenesis, we give a current review of the main DNA-damage repair pathways, with special emphasis in its classification by the kind of mechanisms and in their main features. As a particular case, the error prone repair mechanism is included (SOS-REPAIR). Additionally the three inducible DNA repair systems are described. That is to say, those cases in which the cell treatment with sublethal doses of some physical or chemical agents, induces a cell response that increases its capacity to repair the DNA-damage causes by higher doses of the same agent. Finally some small general comments are made.