The modalities of obligation entailed by civil liability have changed from a sanction- oriented structure motivated by the intention to discipline the wrongdoer (civil liability) to a repairing perspective focused on the victim and her expectation of integral redress (the Law of Damages). Today, anti-juridical behavior has lost its feature of being an assumption to indemnify, and damage is the center of the juridical system, based on the expectation of redress. The ontologic substitution of tools available to administer justice, e.g.: making factors of attribution objective, consideration of futures needs of the victim of the wrong as damage in themselves, and the new contents of what justice administration means (minimization of non-valuable consequences of damages) have profoundly changed all legal implications and the presence of expected damages, being reflected in the Insurance Law due to its most important object which is the risk. In this process, our subject matter adopts new viewpoints that require either putting the most traditional institutions into concepts –for example, the civil liability insurance policy– originated in times in which the duty to repair or the duty of redress exhausted by themselves any legal imposition when determining redress or the substitution of its customary structures for ones that are much more adequate to the common current notion of Justice. We tend to clearly favor the second of these options.